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- 10:41, 8 April 2015 (diff | hist) . . (+126) . . m Compactness
- 10:37, 8 April 2015 (diff | hist) . . (+715) . . m Compactness (→Lemma for a set being compact)
- 08:00, 8 April 2015 (diff | hist) . . (+2,243) . . m Open and closed maps (→Importance with respect to the quotient topology) (current)
- 07:36, 8 April 2015 (diff | hist) . . (+162) . . m Quotient topology
- 07:33, 8 April 2015 (diff | hist) . . (+1,580) . . N Open and closed maps (Created page with "Due to the parallel definitions and other similarities there is little point to having separate pages. ==Definition== ===Open map=== A <math>f:(X,\mathcal{J})\rightarrow (Y,\...")
- 05:15, 8 April 2015 (diff | hist) . . (+16) . . m The relationship between logical implication and the subset relation
- 04:29, 8 April 2015 (diff | hist) . . (-1) . . m Topological space
- 04:28, 8 April 2015 (diff | hist) . . (+115) . . m Topological space
- 19:32, 7 April 2015 (diff | hist) . . (+729) . . N Universal property of the quotient topology (Created page with "==Statement== <math>\require{AMScd} \begin{CD} (X,\mathcal{J}) @>p>> (Y,\mathcal{Q}_p)\\ @VVV @VVfV\\ \searrow @>>f\circ p> (Z,\mathcal{K}) \end{CD}</math>...")
- 12:54, 7 April 2015 (diff | hist) . . (-53) . . m Quotient topology
- 12:48, 7 April 2015 (diff | hist) . . (+948) . . m Quotient topology (→Theorems)
- 12:34, 7 April 2015 (diff | hist) . . (+293) . . m Quotient topology
- 12:29, 7 April 2015 (diff | hist) . . (+611) . . m Quotient topology
- 11:13, 7 April 2015 (diff | hist) . . (+207) . . m Quotient topology
- 10:34, 7 April 2015 (diff | hist) . . (+61) . . N Category:Motivations (Created page with "This category ought to contain all the "motivation for" pages") (current)
- 10:33, 7 April 2015 (diff | hist) . . (+3,807) . . N Motivation for quotient topology (Created page with "This page will discuss informally the motivation for the Quotient topology Quotients (for example {{M|X/\sim}} should already mean "gluing" or "associating" things togeth...") (current)
- 09:23, 7 April 2015 (diff | hist) . . (+40) . . m Main Page
- 09:22, 7 April 2015 (diff | hist) . . (-191) . . m Quotient topology
- 09:22, 7 April 2015 (diff | hist) . . (+271) . . m Quotient topology
- 09:21, 7 April 2015 (diff | hist) . . (+56) . . m Editing guide
- 09:18, 7 April 2015 (diff | hist) . . (-7) . . m Editing guide
- 09:17, 7 April 2015 (diff | hist) . . (+285) . . m Editing guide
- 08:43, 7 April 2015 (diff | hist) . . (+677) . . m Quotient topology
- 07:15, 7 April 2015 (diff | hist) . . (+789) . . m Smooth manifold
- 07:10, 7 April 2015 (diff | hist) . . (+1,536) . . N Smooth structure (Created page with " ==Definition== A smooth structure<ref>Introduction to smooth manifolds - John M Lee - Second Edition</ref> is a '''maximally''' smooth atlas, which recall is...") (current)
- 07:00, 7 April 2015 (diff | hist) . . (+486) . . N Smooth manifold (Created page with " ==Definition== A ''smooth manifold'' is<ref>Introduction to smooth manifolds - John M Lee - Second Edition</ref> a pair {{M|(M,\mathcal{A})}} where {{M|M}} is a Topological...")
- 06:56, 7 April 2015 (diff | hist) . . (+1,597) . . N Smooth atlas (Created page with "'''Note:''' a smooth atlas is a special kind of Atlas ==Definition== An atlas {{M|\mathcal{A} }} is called a ''smooth atlas''<ref>Introduction to smooth manifol...")
- 06:44, 7 April 2015 (diff | hist) . . (+562) . . N Atlas (Created page with "'''Note:''' this page defines an atlas on a Topological manifold which isn't very useful by itself, see Smooth atlas ==Definition== An '''atlas for {{M|M}}'''<ref>Int...") (current)
- 06:41, 7 April 2015 (diff | hist) . . (+459) . . N Diffeomorphism (Created page with "==Definition== A ''diffeomorphism''<ref>Introduction to smooth manifolds - John M Lee - Second Edition</ref> is a special kind of homeomorphism, a function {...") (current)
- 06:38, 7 April 2015 (diff | hist) . . (+688) . . N Smoothly compatible charts (Created page with " ==Definition== Two charts, {{M|(U,\varphi)}} and {{M|(V,\psi)}} are said to be ''smoothly compatible''<ref>Introduction to smooth manifolds - John M Lee - Second Ed...")
- 06:38, 7 April 2015 (diff | hist) . . (+4) . . m Smooth (current)
- 06:33, 7 April 2015 (diff | hist) . . (+14) . . m Transition map (current)
- 06:32, 7 April 2015 (diff | hist) . . (+90) . . m Chart (current)
- 06:20, 7 April 2015 (diff | hist) . . (+989) . . N Transition map (Created page with " ==Definition== Given two charts {{M|(U,\varphi)}} and {{M|(V,\psi)}} on a topological {{M|n-}}manifold where {{M|U\cap V\ne\emptyset}}<ref>Introduction to smooth ma...")
- 06:17, 7 April 2015 (diff | hist) . . (0) . . m Template:N
- 06:16, 7 April 2015 (diff | hist) . . (+72) . . N Template:N (Created page with "<includeonly>{{#if: {{{1|}}} | [math]n-[/math]{{{1}}} | }}</includeonly>")
- 06:10, 7 April 2015 (diff | hist) . . (+50) . . N File:Transition map.JPG (Shows a transition map - using charts in manifolds) (current)
- 06:00, 7 April 2015 (diff | hist) . . (+83) . . m Chart
- 05:59, 7 April 2015 (diff | hist) . . (+51) . . m Manifolds (current)
- 06:52, 6 April 2015 (diff | hist) . . (+2) . . m Span, linear independence, linear dependence, basis and dimension
- 03:18, 6 April 2015 (diff | hist) . . (+13) . . m Manifolds
- 02:41, 6 April 2015 (diff | hist) . . (+866) . . N Smooth (Created page with "'''Note:''' there are many definitions of smooth and it changes a lot between books - I shall be consistent in this wiki and mention the others ==Definition== Here {{M|U\subs...")
- 01:14, 6 April 2015 (diff | hist) . . (+12) . . m Chart
- 01:13, 6 April 2015 (diff | hist) . . (+31) . . m Topological manifold (current)
- 01:13, 6 April 2015 (diff | hist) . . (+88) . . N Manifold (Created page with "May refer to: * Topological manifold * Smooth manifold {{Definition|Manifolds}}") (current)
- 01:12, 6 April 2015 (diff | hist) . . (0) . . m Topological manifold (Alec moved page Manifold to Topological manifold without leaving a redirect)
- 01:10, 6 April 2015 (diff | hist) . . (+1,792) . . N Chart (Created page with "'''Note:''' Sometimes called a coordinate chart ==Definition== A coordinate chart - or just chart on a topological manifold of dimension {{M|n}} is a pair {{M|(U...")
- 00:55, 6 April 2015 (diff | hist) . . (+54) . . m Topological manifold
- 00:51, 6 April 2015 (diff | hist) . . (+1,277) . . N Topological manifold (Created page with "'''Note:''' This page refers to a '''Topological Manifold''' ==Definition== We say {{M|M}} is a ''topological manifold of dimension {{M|n}}'' or simply ''an {{M|n-}}manifold'...")
- 23:48, 5 April 2015 (diff | hist) . . (+87) . . m Set of all derivations of a germ at a point
- 23:47, 5 April 2015 (diff | hist) . . (+1) . . m Index of notation
- 02:55, 5 April 2015 (diff | hist) . . (+731) . . m Index of notation
- 02:34, 5 April 2015 (diff | hist) . . (+38) . . m Tangent space
- 02:33, 5 April 2015 (diff | hist) . . (+2) . . m Set of all derivations of a germ at a point
- 02:32, 5 April 2015 (diff | hist) . . (+683) . . N Set of all derivations of a germ at a point (Created page with "'''Note:''' not to be confused with: Set of all derivations at a point ==Definition== <math>\mathcal{D}_p(\mathbb{R}^n)</math><ref>Loring W. Tu - An introduction to manifo...")
- 02:28, 5 April 2015 (diff | hist) . . (-420) . . m Tangent space
- 02:24, 5 April 2015 (diff | hist) . . (+259) . . m Set of all derivations at a point
- 02:21, 5 April 2015 (diff | hist) . . (+1,109) . . N Derivation (Created page with "'''Warning:''' the definitions below are very similar ==Definition== ===Derivation of <math>C^\infty_p</math>=== A derivation at a point is any Linear map|{{M|\mathbb{R}-}}...")
- 01:51, 5 April 2015 (diff | hist) . . (+2) . . m Set of all derivations at a point (→See also)
- 01:50, 5 April 2015 (diff | hist) . . (+145) . . m The set of all germs of smooth functions at a point (current)
- 01:45, 5 April 2015 (diff | hist) . . (+29) . . N Category:Abstract Algebra Definitions (Created page with "Category:Abstract Algebra")
- 01:44, 5 April 2015 (diff | hist) . . (+431) . . N Equivalence class (Created page with "==Definition== Given an Equivalence relation {{M|\equiv}} the equivalence class of {{M|a}} is denoted as follows: <math>[a]=\{b|a\equiv b\}</math> ==Equivalence relation...")
- 01:41, 5 April 2015 (diff | hist) . . (+649) . . N The set of all germs of smooth functions at a point (Created page with " ==Definition== We usually work in the special case of smooth functions, that will be assumed here (so <math>C^k_p(\mathbb{R}^n)</math> is a notation for this set, but there i...")
- 01:36, 5 April 2015 (diff | hist) . . (+1,676) . . N Germ (Created page with "Germs are an Equivalence class of an Equivalence relation, rather than the usual way of denoting equiv classes we use <math>[f]_p</math> for the germ of {{M|f}} at {{M...") (current)
- 01:19, 5 April 2015 (diff | hist) . . (+61) . . m Index of notation
- 01:18, 5 April 2015 (diff | hist) . . (+1,288) . . N Set of all derivations at a point (Created page with "I chose to denote this (as in<ref>Loring W. Tu - An introduction to manifolds - Second edition</ref>) by <math>\mathcal{D}_p(A)</math> however at least one other author<ref>Jo...")
- 01:00, 5 April 2015 (diff | hist) . . (+191) . . m Index of notation
- 00:57, 5 April 2015 (diff | hist) . . (+723) . . N Leibniz rule (Created page with "==Definition== A function <math>f:A\rightarrow B</math> is said to satisfy the Leibniz rule<ref>Introduction to Smooth Manifolds - Second Edition - John M Lee</ref><ref>An int...") (current)
- 00:48, 5 April 2015 (diff | hist) . . (+1,133) . . m Tangent space
- 00:35, 5 April 2015 (diff | hist) . . (+1,482) . . N Manifolds (Created page with " Consider the Earth, the planet you are on right now. Locally you can go forward and back, left and right - you may move around the surface as if it were a plane. Of course it...")
- 00:26, 5 April 2015 (diff | hist) . . (+16) . . m Main Page
- 00:25, 5 April 2015 (diff | hist) . . (+22) . . N Category:Manifolds Definitions (Created page with "Category:Manifolds") (current)
- 00:25, 5 April 2015 (diff | hist) . . (+21) . . N Category:Manifolds (Created page with "Category:Subjects") (current)
- 00:24, 5 April 2015 (diff | hist) . . (+1,319) . . N Tangent space (Created page with "I prefer to denote the tangent space (of a set {{M|A}} at a point {{M|p}}) by {{M|T_p(A)}} - as this involves the letter T for tangent however one author<ref>John M. Lee - Int...")
- 00:13, 5 April 2015 (diff | hist) . . (+957) . . m Index of notation
- 21:01, 30 March 2015 (diff | hist) . . (+6) . . m The arc length of a regular parametrisation is smooth (current)
- 21:00, 30 March 2015 (diff | hist) . . (+110) . . N The arc length of a regular parametrisation is smooth (Created page with "<ref>Elementary Differential Geometry - Second Edition - Springer SUMS series - Pressley</ref> ==References==")
- 20:59, 30 March 2015 (diff | hist) . . (+74) . . m Arc length (current)
- 00:47, 30 March 2015 (diff | hist) . . (+41) . . m Main Page
- 00:20, 30 March 2015 (diff | hist) . . (+1,080) . . N Chain rule (Created page with " ==Definition== ===1 dimensional case=== Here {{M|f(x)}} and {{M|g(t)}} are functions: <math>\frac{d}{dt}\Big[f\circ g\Big]=\left.\frac{df}{dx}\right|_{g(t)}\frac{dg}{dt}</ma...") (current)
- 22:24, 29 March 2015 (diff | hist) . . (-1,191) . . m Parametrisation
- 22:24, 29 March 2015 (diff | hist) . . (+1,771) . . N Arc length (Created page with "Arc length of curves here is defined with respect to parametrisations - it is fundamental for defining Unit speed parametrisation|unit speed pa...")
- 22:21, 29 March 2015 (diff | hist) . . (+17) . . m Differential Geometry
- 22:20, 29 March 2015 (diff | hist) . . (+324) . . N Unit speed parametrisation (Created page with "A unit speed Parametrisation requires knowledge of Reparametrisation and Regular curve ==Definition== A unit speed parametrisation {{M|\gamma}} is a Parametrisa...")
- 22:15, 29 March 2015 (diff | hist) . . (+37) . . N User talk:Alec (Created page with "Still waiting for that first message!")
- 22:15, 29 March 2015 (diff | hist) . . (+109) . . N User:Alec (Created page with "Hi, I'm the admin of this site and creator of most of the content. Write a note on my talk page for requests!")
- 22:14, 29 March 2015 (diff | hist) . . (+166) . . N Differential Geometry (Created page with "First steps: * Curve * Parametrisation * Reparametrisation * Regular curve * Unit speed parametrisation Category:Differential Geometry")
- 22:13, 29 March 2015 (diff | hist) . . (+28) . . m Main Page
- 22:12, 29 March 2015 (diff | hist) . . (+1,546) . . m Regular curve (current)
- 21:29, 29 March 2015 (diff | hist) . . (+55) . . m Regular curve
- 20:58, 29 March 2015 (diff | hist) . . (+1) . . m Reparametrisation
- 20:57, 29 March 2015 (diff | hist) . . (+727) . . N Reparametrisation (Created page with "This page requires knowledge of a parametrisation of a curve ==Definition== A function {{M|\tilde{\gamma}:(\tilde{a},\tilde{b})\rightarrow\mathb...")
- 02:20, 29 March 2015 (diff | hist) . . (+28) . . N Category:Vector Analysis Definitions (Created page with "Category:Vector Analysis") (current)
- 02:20, 29 March 2015 (diff | hist) . . (+21) . . N Category:Vector Analysis (Created page with "Category:Subjects") (current)
- 02:04, 29 March 2015 (diff | hist) . . (+534) . . N Vector dot product (Created page with "The vector dot product - sometimes called the scalar product, or inner product is defined as follows: ==Definition== Given two vectors in a finite vector space {{M|a,b\in V}}...") (current)
- 01:32, 29 March 2015 (diff | hist) . . (+17) . . m Index of notation
- 01:32, 29 March 2015 (diff | hist) . . (+55) . . m Index of notation
- 21:54, 28 March 2015 (diff | hist) . . (+21) . . N Category:Geometry of Curves and Surfaces (Created page with "Category:Subjects") (current)
- 21:53, 28 March 2015 (diff | hist) . . (+44) . . N Category:Geometry of Curves and Surfaces Definitions (Created page with "Category:Geometry of Curves and Surfaces") (current)
- 21:52, 28 March 2015 (diff | hist) . . (+2,379) . . N Parametrisation (Created page with " ==Definition== A parametrisation {{M|\gamma}} is a function<ref>Elementary Differential Geometry - Pressley - Springer SUMS</ref>: <math>\gamma:(a,b)\rightarrow\mathbb{R}^n<...")
- 21:30, 28 March 2015 (diff | hist) . . (+550) . . m Curve (current)
- 21:15, 28 March 2015 (diff | hist) . . (+34) . . N Category:Differential Geometry Definitions (Created page with "Category:Differential Geometry") (current)
- 01:41, 28 March 2015 (diff | hist) . . (+612) . . m Measure Theory (→Our first measure) (current)
- 19:18, 25 March 2015 (diff | hist) . . (+834) . . N Curve (Created page with "A curve can mean many things. It is reasonably standard to say however that a curve is any one dimensional "thing" ==Definitions== ===Level curve=== Given a <math>f:\mathbb{R...")
- 18:47, 25 March 2015 (diff | hist) . . (-26) . . m Regular curve (→See also)
- 18:45, 25 March 2015 (diff | hist) . . (+3) . . m Regular curve (→See also)
- 18:43, 25 March 2015 (diff | hist) . . (+47) . . m Regular curve
- 18:41, 25 March 2015 (diff | hist) . . (+21) . . N Category:Differential Geometry (Created page with "Category:Subjects") (current)
- 10:18, 22 March 2015 (diff | hist) . . (+1,845) . . m Measurable map
- 14:41, 20 March 2015 (diff | hist) . . (+282) . . m Random variable (current)
- 14:18, 20 March 2015 (diff | hist) . . (+213) . . m Random variable
- 14:00, 20 March 2015 (diff | hist) . . (0) . . m Template:Begin Example (current)
- 14:00, 20 March 2015 (diff | hist) . . (+217) . . m Editing guide
- 13:57, 20 March 2015 (diff | hist) . . (+123) . . N Template:End Example (Created page with "<includeonly></div></includeonly> <noinclude> See Editing guide - Examples for info </noinclude>") (current)
- 13:57, 20 March 2015 (diff | hist) . . (+123) . . N Template:End Example Body (Created page with "<includeonly></div></includeonly> <noinclude> See Editing guide - Examples for info </noinclude>") (current)
- 13:56, 20 March 2015 (diff | hist) . . (+162) . . N Template:Begin Example Body (Created page with "<includeonly></b><div class="mw-collapsible-content"><hr/></includeonly> <noinclude> See Editing guide - Examples for info </noinclude>") (current)
- 13:55, 20 March 2015 (diff | hist) . . (+190) . . N Template:Begin Example (Created page with "<includeonly><div class="toccolours mw-collapsible mw-collapsed" style="width:99%"><b></includeonly> <noinclude> See Editing guide - Examples for in...")
- 09:02, 19 March 2015 (diff | hist) . . (+2,647) . . m Random variable
- 08:16, 19 March 2015 (diff | hist) . . (+1,910) . . m Probability space
- 20:03, 18 March 2015 (diff | hist) . . (+326) . . m Random variable
- 19:32, 18 March 2015 (diff | hist) . . (+65) . . m Probability space
- 19:31, 18 March 2015 (diff | hist) . . (+72) . . m Probability space
- 19:30, 18 March 2015 (diff | hist) . . (+7) . . m Probability space
- 19:28, 18 March 2015 (diff | hist) . . (+228) . . N Probability space (Created page with "==Definition== Given a measure space {{M|(X,\mathcal{A},\mu)}} We call it a probability space if <math>\mu</math> is a probability measure, which means tha...")
- 17:25, 18 March 2015 (diff | hist) . . (+10) . . m Abstract Algebra (current)
- 15:48, 18 March 2015 (diff | hist) . . (+210) . . N Random variable (Created page with "==Definition== A '''Random variable''' is a measurable map from a probability space to any measurable space {{Def...")
- 15:37, 18 March 2015 (diff | hist) . . (+2) . . m Measurable map
- 15:36, 18 March 2015 (diff | hist) . . (+317) . . N Measurable map (Created page with "==Definition== Let {{M|(X,\mathcal{A})}} and {{M|(X',\mathcal{A}')}} be measurable spaces Then a map <math>T:X\rightarrow X'</math> is called '''<math>\m...")
- 14:29, 18 March 2015 (diff | hist) . . (+301) . . N Measures are monotonic and subtractive (Created page with "==Theorem== A measure (or pre-measure) is monotonic and subtractive<ref>p37 - Halmos - Meas...")
- 14:24, 18 March 2015 (diff | hist) . . (+409) . . N Subtractive set function (Created page with "==Definition== A set function <math>f:E\rightarrow[0,\infty]\subset\mathbb{R}\cup\{-\infty,\infty\}</math> is subtractive<ref>p37 - Halmos - Measure Theory - Graduate Texts in...") (current)
- 14:18, 18 March 2015 (diff | hist) . . (+548) . . N Monotonic set function (Created page with "Sometimes called '''Monotone set function'''. ==Definition== A set function {{M|f:E\rightarrow [0,\infty]\subset\mathbb{R} }} is '''monotonic'''<ref> p37 - Halmos, Measure T...") (current)
- 14:10, 18 March 2015 (diff | hist) . . (+134) . . m Measure (→Terminology)
- 14:09, 18 March 2015 (diff | hist) . . (+962) . . m Measure
- 13:33, 18 March 2015 (diff | hist) . . (-9) . . m Index of notation
- 13:28, 18 March 2015 (diff | hist) . . (+28) . . m Complement (current)
- 13:04, 18 March 2015 (diff | hist) . . (+394) . . m Ring
- 12:46, 18 March 2015 (diff | hist) . . (+1,692) . . N Ring (Created page with "Not to be confused with rings of sets which are a topic of algebras of sets and thus Algebras}} and Sigma-ring...")
- 20:25, 17 March 2015 (diff | hist) . . (+698) . . N Complement (Created page with "{{Extra Maths}} ==Definition== The complement of a set is everything not in it. For example given a set {{M|A}} in a space {{M|X}} the complement of {{M|A}} (often denoted {{M...")
- 21:12, 16 March 2015 (diff | hist) . . (+832) . . m Measure Theory
- 20:34, 16 March 2015 (diff | hist) . . (+1,572) . . N Ring generated by (Created page with "Here ring refers to a ring of sets ==Definition== Given any class of sets {{M|A}}, there exists a unique ring {{M|R_0}} such that {{M|E\subseteq R_0}} and su...")
- 20:19, 16 March 2015 (diff | hist) . . (+877) . . m Ring of sets
- 20:10, 16 March 2015 (diff | hist) . . (-16) . . m Measure Theory
- 20:01, 16 March 2015 (diff | hist) . . (+345) . . m Ring of sets
- 23:13, 15 March 2015 (diff | hist) . . (+170) . . N Outer-measure (Created page with " ==Definition== <math>\mu^*=\text{Inf}\left\{\sum^\infty_{n=1}\mu(E_n)|E_n\in R\ \forall n,\ E\subset\bigcup^\infty_{n=1}E_n\right\}</math> {{Definition|Measure Theory}}")
- 21:11, 15 March 2015 (diff | hist) . . (+2,241) . . m Measure Theory
- 19:08, 15 March 2015 (diff | hist) . . (+477) . . m Measure Theory
- 18:33, 15 March 2015 (diff | hist) . . (+2) . . m Lebesgue measure
- 18:32, 15 March 2015 (diff | hist) . . (+346) . . m Lebesgue measure
- 18:30, 15 March 2015 (diff | hist) . . (+23) . . m Measure
- 18:27, 15 March 2015 (diff | hist) . . (+545) . . m Measure
- 18:22, 15 March 2015 (diff | hist) . . (-3) . . m Measure space
- 18:21, 15 March 2015 (diff | hist) . . (+217) . . N Measurable space (Created page with " ==Definition== Let {{M|X}} be a set and {{M|\mathcal{A} }} a algebra}}, then {{M|(X,\mathcal{A})}} is a ''Measurable space'' ==See also== * Meas...")
- 18:21, 15 March 2015 (diff | hist) . . (-128) . . m Measure space
- 18:08, 15 March 2015 (diff | hist) . . (+3,014) . . N Coset (Created page with " ==Definition== Let {{M|(G,\times)}} be a group and {{M|(H,\times)}} a subgroup we denote cosets as follows: Given any <math>g\in G</math> the * '''Lef...") (current)
- 17:35, 15 March 2015 (diff | hist) . . (+1,418) . . m Subgroup (current)
- 17:23, 15 March 2015 (diff | hist) . . (+434) . . N Subgroup (Created page with "A subgroup {{M|(H,\times_H:H\times H\rightarrow H}} of a Group {{M|(G,\times_G:G\times G\rightarrow G)}} is a set {{M|H\subseteq G}} which is a group under the o...")
- 17:19, 15 March 2015 (diff | hist) . . (+14) . . m Abstract Algebra
- 21:03, 14 March 2015 (diff | hist) . . (+436) . . m Pre-measure
- 19:43, 14 March 2015 (diff | hist) . . (+1,655) . . m Ordering
- 18:10, 14 March 2015 (diff | hist) . . (+446) . . N Talk:Ordering (Created page with "==Scrap current page and re-write== I wrote this page initially when I first encountered orders formally and there are.... it's not brilliantly written and beyond repair (larg...") (current)
- 22:35, 13 March 2015 (diff | hist) . . (+193) . . m Index of notation
- 22:32, 13 March 2015 (diff | hist) . . (+20) . . m Measure
- 22:31, 13 March 2015 (diff | hist) . . (-2) . . m Template:Extra Maths
- 22:30, 13 March 2015 (diff | hist) . . (+6) . . m Template:Extra Maths
- 22:28, 13 March 2015 (diff | hist) . . (+3) . . m Template:Extra Maths
- 22:26, 13 March 2015 (diff | hist) . . (+164) . . N Template:Extra Maths (Created page with "<includeonly> <math>\newcommand{\udot}{\bigcup\mkern-13.5mu\cdot\mkern5mu}</math> <math>\newcommand{\bigudot}{\cup\mkern-11.5mu\cdot\mkern5mu}</math> </includeonly>")
- 18:31, 13 March 2015 (diff | hist) . . (+428) . . N Lebesgue measure (Created page with " ==Definition== The set function <math>\lambda^n:(\mathbb{R}^n,\mathcal{B}(\mathbb{R}^n))\rightarrow\mathbb{R}_{\ge}</math><ref>P27 - Measures, Integrals and Martingales - Re...")
- 18:08, 13 March 2015 (diff | hist) . . (+66) . . m Measure
- 18:08, 13 March 2015 (diff | hist) . . (+49) . . m Pre-measure
- 18:05, 13 March 2015 (diff | hist) . . (+31) . . m Measure space
- 18:04, 13 March 2015 (diff | hist) . . (+229) . . m Index of notation
- 17:58, 13 March 2015 (diff | hist) . . (+996) . . N Measure (Created page with "Not to be confused with Pre-measure ==Definition== A ring}} {{M|\mathcal{A} }} and a countably additive, Extended real val...")
- 17:46, 13 March 2015 (diff | hist) . . (+949) . . N Pre-measure (Created page with " ==Definition== A pre-measure (often denoted {{M|\mu_0}}) is the precursor to a measure which are often denoted {{M|\mu}} A pre-measure is a ring...")
- 16:54, 13 March 2015 (diff | hist) . . (-43) . . m Additive function (→Countable additivity can imply additivity)
- 16:44, 13 March 2015 (diff | hist) . . (+2,754) . . N Additive function (Created page with "An additive function is a homomorphism that preserves the operation of addition in place on the structure in question. In group theory (because there's only...")
- 16:39, 13 March 2015 (diff | hist) . . (+644) . . N Mathjax bug (Created page with "<pre> f(\sum^\infty_{n=1}b_n)= \begin{array} f(\sum^n_{i=1}a_i) \\ \sum^\infty_{n=1}f(b_n)=\sum^n_{i=1}f(a_i)+f(0)=\sum^n_{i=1}f(a_i) \end{array} </pre> produces: <math>f(\...") (current)
- 16:10, 13 March 2015 (diff | hist) . . (+355) . . N Set function (Created page with " ==Definition== A set function is simply a function with a domain of definition that is a class of sets<ref>Halmos - Measure Theory - p30 - Springer - Graduate Te...") (current)
- 16:07, 13 March 2015 (diff | hist) . . (+2,454) . . N Extended real value (Created page with "If a function is described as "extended real valued" it means: <math>f:X\rightarrow \mathbb{R}\cup\{-\infty,+\infty\}</math> ==Definition== The set <math>\mathb...") (current)
- 15:49, 13 March 2015 (diff | hist) . . (+409) . . N Index of terms (Created page with " {| class="wikitable" border="1" |- ! Term ! Context ! Meaning |- | Extended real value | * Measure Theory | Refers to the set <math>\mathbb{R}\cup\{+\infty,-\infty\}</ma...") (current)
- 15:46, 13 March 2015 (diff | hist) . . (+21) . . m Main Page
- 15:42, 13 March 2015 (diff | hist) . . (+123) . . N Measure Theory (Created page with "==First things== * Ring of sets * Algebra of sets * Sigma-ring * Sigma-algebra Category:Measure Theory")
- 15:41, 13 March 2015 (diff | hist) . . (+21) . . m Main Page
- 15:40, 13 March 2015 (diff | hist) . . (-3) . . m Measure space
- 15:39, 13 March 2015 (diff | hist) . . (+738) . . N Sigma-algebra (Created page with "A '''Sigma-algebra''' of sets, or {{sigma|algebra}} is very similar to a ring}} of sets. Like how ring of sets and Algebra of sets|...")
- 15:34, 13 March 2015 (diff | hist) . . (+728) . . N Sigma-ring (Created page with "A '''Sigma-ring''' or <math>\sigma</math>-ring, is closely related to rings of sets, and just like algebras of sets are related to rings o...") (current)
- 15:30, 13 March 2015 (diff | hist) . . (+55) . . N Template:Sigma (Created page with "<includeonly><math>\sigma</math>-{{{1|}}}</includeonly>")
- 15:21, 13 March 2015 (diff | hist) . . (+816) . . N Algebra of sets (Created page with "An Algebra of sets is sometimes called a '''Boolean algebra''' We will show later that every Algebra of sets is an Algebra of sets ==Definition== An class {{M|R}} of set...")
- 15:12, 13 March 2015 (diff | hist) . . (+751) . . N Ring of sets (Created page with "A Ring of sets is also known as a '''Boolean ring''' Note that every Algebra of sets is also a ring, and that an Algebra of sets is sometimes called a '''Boolean alge...")
- 14:35, 12 March 2015 (diff | hist) . . (+719) . . m Ordering
- 14:17, 12 March 2015 (diff | hist) . . (+302) . . N Well-ordering (Created page with "A well-ordering is a special kind of ordering ==Definition== An ordering <math><</math> of a set {{M|P}} which is both: * Linear (total) * strict Is a ''well-or...")
- 14:02, 12 March 2015 (diff | hist) . . (+774) . . N Regular curve (Created page with " ==Definition== A curve <math>\gamma:\mathbb{R}\rightarrow\mathbb{R}^3</math> usually (however <math>\gamma:A\subseteq\mathbb{R}\rightarrow\mathbb{R}^n</math> more generally)...")
- 13:53, 12 March 2015 (diff | hist) . . (+388) . . N Matrix (Created page with " ==Definition== An m-by-n matrix has {{M|m}} rows and {{M|n}} columns - I've always had trouble remembering this, which is why I write it down. <math>\begin{pmatrix} a_{11}...") (current)
- 13:45, 12 March 2015 (diff | hist) . . (+2,295) . . N Jacobian (Created page with "Sometimes called "Jacobian Matrix", or "differential". ==Common definition== Given a function <math>f:\mathbb{R}^m\rightarrow\mathbb{R}^n</math> (I use the conve...") (current)
- 10:51, 12 March 2015 (diff | hist) . . (+446) . . m Index of notation
- 10:25, 12 March 2015 (diff | hist) . . (+1,839) . . N Cardinality (Created page with "Informally the cardinality of a set is the number of things in it. The cardinality of a set {{M|A}} is denoted <math>|A|</math> ==Equipotent cardinality (<math>|A|=|B|</math...") (current)
- 09:45, 12 March 2015 (diff | hist) . . (+1,144) . . m Ordering
- 18:17, 11 March 2015 (diff | hist) . . (+329) . . m Group
- 18:00, 11 March 2015 (diff | hist) . . (+421) . . m Group (→Cancellation laws)
- 14:48, 11 March 2015 (diff | hist) . . (+3) . . m Template:Begin Theorem
- 14:48, 11 March 2015 (diff | hist) . . (+4) . . m Template:Begin Proof
- 14:47, 11 March 2015 (diff | hist) . . (0) . . m Template:Begin Proof
- 14:45, 11 March 2015 (diff | hist) . . (+5) . . m Template:Begin Proof
- 14:43, 11 March 2015 (diff | hist) . . (+1,176) . . m Ordered pair
- 14:28, 11 March 2015 (diff | hist) . . (-1) . . m Group
- 14:19, 11 March 2015 (diff | hist) . . (-51) . . m Group
- 14:18, 11 March 2015 (diff | hist) . . (+16) . . m Group
- 14:13, 11 March 2015 (diff | hist) . . (+8) . . m Group
- 13:58, 11 March 2015 (diff | hist) . . (+23) . . m Main Page
- 13:09, 11 March 2015 (diff | hist) . . (+3,333) . . m Group
- 12:37, 11 March 2015 (diff | hist) . . (+573) . . m Group
- 10:25, 11 March 2015 (diff | hist) . . (+97) . . m Set theory axioms (current)
- 10:15, 11 March 2015 (diff | hist) . . (+581) . . m Group
- 10:03, 11 March 2015 (diff | hist) . . (+1) . . m Group (→Identity is unique)
- 10:01, 11 March 2015 (diff | hist) . . (+433) . . m Group
- 09:47, 11 March 2015 (diff | hist) . . (+22) . . m Template:End Theorem (current)
- 09:47, 11 March 2015 (diff | hist) . . (-2) . . m Template:End Proof (current)
- 09:46, 11 March 2015 (diff | hist) . . (-2) . . m Template:Begin Proof
- 09:45, 11 March 2015 (diff | hist) . . (-2) . . m Template:Begin Theorem
- 09:44, 11 March 2015 (diff | hist) . . (0) . . m Template:Begin Theorem
- 09:44, 11 March 2015 (diff | hist) . . (-1) . . m Template:Begin Theorem
- 09:43, 11 March 2015 (diff | hist) . . (+1) . . m Template:Begin Theorem
- 09:43, 11 March 2015 (diff | hist) . . (0) . . m Template:Begin Theorem
- 09:42, 11 March 2015 (diff | hist) . . (-2) . . m Template:Begin Theorem
- 09:41, 11 March 2015 (diff | hist) . . (0) . . m Template:Begin Theorem
- 09:41, 11 March 2015 (diff | hist) . . (+24) . . m Template:Begin Theorem
- 09:40, 11 March 2015 (diff | hist) . . (+24) . . m Template:Begin Proof
- 09:40, 11 March 2015 (diff | hist) . . (+24) . . m Template:End Proof
- 09:39, 11 March 2015 (diff | hist) . . (+101) . . N Template:End Proof (Created page with "<includeonly> </div> </includeonly> See Editing guide - Theorems for info")
- 09:38, 11 March 2015 (diff | hist) . . (+131) . . N Template:Begin Proof (Created page with "<includeonly> <div class="mw-collapsible-content"> </includeonly> See Editing guide - Theorems for info")
- 09:38, 11 March 2015 (diff | hist) . . (0) . . m Template:End Theorem
- 09:35, 11 March 2015 (diff | hist) . . (0) . . m Template:Begin Theorem
- 09:35, 11 March 2015 (diff | hist) . . (0) . . m Template:End Theorem
- 09:34, 11 March 2015 (diff | hist) . . (0) . . m Template:End Theorem (Alec moved page Template:EndTheorem to Template:End Theorem without leaving a redirect)
- 09:33, 11 March 2015 (diff | hist) . . (+101) . . N Template:End Theorem (Created page with "<includeonly> </div> </includeonly> See Editing guide - Theorems for info")
- 09:32, 11 March 2015 (diff | hist) . . (+190) . . m Editing guide
- 09:31, 11 March 2015 (diff | hist) . . (+167) . . N Template:Begin Theorem (Created page with "<includeonly> <div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> </includeonly> See Editing guide - Theorems for info")
- 09:28, 11 March 2015 (diff | hist) . . (+764) . . N Group (Created page with "==Definition== A group is a set {{M|G}} and an operation <math>*:G\times G\rightarrow G</math>, denoted <math>(G,*:G\times G\rightarrow G)</math> but Mathematicians are lazy...")
- 08:38, 11 March 2015 (diff | hist) . . (+21) . . N Category:Abstract Algebra (Created page with "Category:Subjects") (current)
- 08:37, 11 March 2015 (diff | hist) . . (+64) . . N Abstract Algebra (Created page with "*Group *Coset *Field Category:Abstract Algebra")
- 00:25, 11 March 2015 (diff | hist) . . (+146) . . m Set theory axioms
- 00:10, 11 March 2015 (diff | hist) . . (+30) . . m Ordered pair
- 00:09, 11 March 2015 (diff | hist) . . (+275) . . m Set theory axioms
- 23:51, 10 March 2015 (diff | hist) . . (+428) . . m Set theory axioms
- 16:36, 9 March 2015 (diff | hist) . . (+171) . . N Template:Bad Page (Created page with "<includeonly> Category:Bad Pages '''WARNING:''' this is a bad page - it is little more than "my notes", it could be wrong and should not be relied upon. </includeonly>") (current)
- 16:35, 9 March 2015 (diff | hist) . . (+1) . . m Formal logic language (current)
- 16:35, 9 March 2015 (diff | hist) . . (+12) . . m Formal logic language
- 15:03, 9 March 2015 (diff | hist) . . (+941) . . m Formal logic language
- 14:49, 9 March 2015 (diff | hist) . . (+1,354) . . N Formal logic language (Created page with "==Introduction== Formal logic plays an important role, especially so in set theory, but overall an important role. It is important to have a concrete understanding of this. =...")
- 00:29, 9 March 2015 (diff | hist) . . (+695) . . m Closed set
- 00:23, 9 March 2015 (diff | hist) . . (+31) . . m Open set
- 00:22, 9 March 2015 (diff | hist) . . (+11) . . m Limit point
- 00:20, 9 March 2015 (diff | hist) . . (0) . . m Closure, interior and boundary (Alec moved page Closure, Interior and boundary to Closure, interior and boundary without leaving a redirect) (current)
- 00:19, 9 March 2015 (diff | hist) . . (+969) . . m Open ball
- 23:32, 8 March 2015 (diff | hist) . . (+108) . . m Open set
- 22:45, 8 March 2015 (diff | hist) . . (+429) . . N Metric subspace (Created page with "==Definition== Given a metric space {{M|(X,d)}} and any {{M|A\subset X}}, we can define a metric as follows: <math>d_A:A\times A\rightarrow\mathbb{R}</math>...")
- 22:40, 8 March 2015 (diff | hist) . . (+808) . . m Sequential compactness
- 22:26, 8 March 2015 (diff | hist) . . (+723) . . N Sequential compactness (Created page with "The Bolzano-Weierstrass theorem states that every bounded sequence has a convergent subsequence. Sequential compactness extends this notion to general topolo...")
- 22:03, 8 March 2015 (diff | hist) . . (+53) . . m Compactness
- 17:21, 8 March 2015 (diff | hist) . . (+260) . . m Linear map
- 17:17, 8 March 2015 (diff | hist) . . (+130) . . m Vector space
- 17:16, 8 March 2015 (diff | hist) . . (+114) . . m Span, linear independence, linear dependence, basis and dimension
- 17:13, 8 March 2015 (diff | hist) . . (-1,242) . . m Sequence
- 17:12, 8 March 2015 (diff | hist) . . (+2,004) . . N Convergence of a sequence (Created page with "Like with continuity there are three forms for convergence of a Sequence Given a sequence <math>(a_n)^n_{n=1}</math> we may say that it converges to {{...")
- 17:10, 8 March 2015 (diff | hist) . . (-650) . . m Cauchy criterion for convergence (Wasn't an example of Cauchy criterion for convergence)
- 16:59, 8 March 2015 (diff | hist) . . (+63) . . m Main Page
- 16:58, 8 March 2015 (diff | hist) . . (+22) . . m Topology
- 16:58, 8 March 2015 (diff | hist) . . (+22) . . m Linear Algebra (current)
- 16:57, 8 March 2015 (diff | hist) . . (+199) . . N Linear Algebra (Created page with "This is a guide to the pages in the Linear Algebra category *Discussion on change of basis, basis and coordinates C...")
- 16:54, 8 March 2015 (diff | hist) . . (+1,125) . . m Basis and coordinates
- 16:45, 8 March 2015 (diff | hist) . . (+55) . . N File:Non orthagonal example.JPG (This is the second example in Basis and coordinates) (current)
- 16:36, 8 March 2015 (diff | hist) . . (+34) . . m Basis and coordinates
- 16:35, 8 March 2015 (diff | hist) . . (+3,148) . . m Basis and coordinates (Still need to proof read.)
- 15:52, 8 March 2015 (diff | hist) . . (+4,434) . . N Basis and coordinates (Done initial version)
- 15:21, 8 March 2015 (diff | hist) . . (+53) . . N File:Coordinate example.JPG (A picture I drew for use on Basis and coordinates) (current)
- 13:40, 8 March 2015 (diff | hist) . . (+131) . . m Example comparing bilinear to linear maps
- 04:52, 8 March 2015 (diff | hist) . . (+299) . . m Sequence
- 04:44, 8 March 2015 (diff | hist) . . (+1,116) . . N Cauchy criterion for convergence (Created page with "If a sequence converges, it is the same as saying it matches the Cauchy criterion for convergence. ==Cauchy Sequence== A sequence <math>(a_n)^\infty_{n=1}</math>...")
- 04:36, 8 March 2015 (diff | hist) . . (+12) . . Norm (Forgot power!)
- 04:33, 8 March 2015 (diff | hist) . . (+57) . . N Category:Functional Analysis Definitions (Created page with "Category:Functional Analysis Category:Definitions") (current)
- 04:32, 8 March 2015 (diff | hist) . . (+21) . . N Category:Functional Analysis (Created page with "Category:Subjects") (current)
- 04:31, 8 March 2015 (diff | hist) . . (+54) . . N Category:Functional Analysis Theorems (Created page with "Category:Theorems Category:Functional Analysis") (current)
- 04:26, 8 March 2015 (diff | hist) . . (+1,821) . . N Sequence (Created page with " ==Introduction== A sequence is one of the earliest and easiest definitions encountered, but I will restate it. I was taught to denote the sequence <math>\{a_1,a_2,...\}</ma...")
- 04:25, 8 March 2015 (diff | hist) . . (+100) . . m Template:Definition
- 04:04, 8 March 2015 (diff | hist) . . (+130) . . m Norm
- 03:55, 8 March 2015 (diff | hist) . . (+446) . . N Pullback norm (Created page with "==Definition== Suppose we have a normed vector space, <math>(V,\|\cdot\|_V,F)</math> and another vector space {{M|(U,F)}} and a Linear map|linear i...")
- 03:51, 8 March 2015 (diff | hist) . . (+41) . . m Linear isometry
- 03:51, 8 March 2015 (diff | hist) . . (+183) . . m Norm
- 03:48, 8 March 2015 (diff | hist) . . (+179) . . m Norm
- 03:47, 8 March 2015 (diff | hist) . . (+78) . . m Vector space
- 03:42, 8 March 2015 (diff | hist) . . (+1,159) . . N Linear isometry (Created page with "==Definition== Suppose {{M|U}} and {{M|V}} are normed vector spaces with the norm <math>\|\cdot\|_U</math> and </math>\|\cdot\|_V</math> respectively...")
- 03:42, 8 March 2015 (diff | hist) . . (+104) . . m Linear map
- 03:41, 8 March 2015 (diff | hist) . . (+145) . . m Linear map
- 03:29, 8 March 2015 (diff | hist) . . (+90) . . m Norm
- 03:28, 8 March 2015 (diff | hist) . . (+22) . . m Vector space
- 03:27, 8 March 2015 (diff | hist) . . (-2) . . m Vector space
- 03:26, 8 March 2015 (diff | hist) . . (0) . . m Span, linear independence, linear dependence, basis and dimension (Alec moved page Span, basis and dimension to Span, linear independence, linear dependence, basis and dimension without leaving a redirect)
- 03:25, 8 March 2015 (diff | hist) . . (+49) . . N Category:Linear Algebra Theorems (Created page with "Category:Theorems Category:Linear Algebra")
- 03:25, 8 March 2015 (diff | hist) . . (+982) . . N Euclidean norm (Created page with "This is an example of a Norm ==Definition== The Euclidean norm is denoted <math>\|\cdot\|_2</math> is a norm on <math>\mathbb{R}^n</math> Here for <math>x\in\mathbb{R}^n...")
- 03:22, 8 March 2015 (diff | hist) . . (-886) . . m Norm
- 03:17, 8 March 2015 (diff | hist) . . (+737) . . m Norm (Made common norms into table and expanded it)
- 03:04, 8 March 2015 (diff | hist) . . (+587) . . m Norm
- 02:58, 8 March 2015 (diff | hist) . . (+733) . . m Index of notation
- 02:47, 8 March 2015 (diff | hist) . . (+205) . . m Index of notation
- 02:40, 8 March 2015 (diff | hist) . . (+118) . . m Span, linear independence, linear dependence, basis and dimension
- 02:38, 8 March 2015 (diff | hist) . . (+1,317) . . Span, linear independence, linear dependence, basis and dimension (Added basis.)
- 02:27, 8 March 2015 (diff | hist) . . (-6) . . m Category:Linear Algebra (current)
- 02:27, 8 March 2015 (diff | hist) . . (+4) . . m Category:Linear Algebra
- 00:43, 8 March 2015 (diff | hist) . . (+302) . . N Span, linear independence, linear dependence, basis and dimension (Created page with " ==Span== ===Definition=== Given a set of vectors {{M|S}} in a vector space {{M|(V,F)}} <math>\text{Span}(S)=\{\sum^n_{i=1}\lambda v_i|n\in\mathbb{N},\ v_i\in S,\ \lambda_i\i...")
- 23:55, 7 March 2015 (diff | hist) . . (+104) . . m Index of notation
- 23:53, 7 March 2015 (diff | hist) . . (+24) . . m Main Page
- 23:53, 7 March 2015 (diff | hist) . . (+794) . . N Index of notation (Created page with "Ordered symbols are notations which are (likely) to appear as they are given here, for example <math>C([a,b],\mathbb{R})</math> denotes the continuous function on the interval...")
- 17:29, 7 March 2015 (diff | hist) . . (+43) . . m Norm
- 17:27, 7 March 2015 (diff | hist) . . (+566) . . Norm (Added proof and common norms)
- 17:15, 7 March 2015 (diff | hist) . . (+672) . . m Norm
- 17:03, 7 March 2015 (diff | hist) . . (+2,451) . . N Cauchy-Schwarz inequality (Created page with "==Statement== For any <math>a_1,...,a_n,b_1,...,b_n\in\mathbb{R}\ </math> we will have<br/> <math>\sum^n_{i=1}a_ib_i\le\sqrt{\sum^n_{i=1}a_i^2}\sqrt{\sum^n_{i=1}b_i^2}</math>...")
- 16:35, 7 March 2015 (diff | hist) . . (+48) . . N Category:Real Analysis Theorems (Created page with "Category:Real Analysis Category:Theorems") (current)
- 16:31, 7 March 2015 (diff | hist) . . (+128) . . N Category:Useful inequalities (Created page with "This category is intended to capture any useful inequalities, they '''should''' all be listed on Useful inequalities however") (current)
- 16:31, 7 March 2015 (diff | hist) . . (+314) . . N Useful inequalities (Created page with "Category:Useful inequalities Here is a list of useful inequalities: {| class="wikitable" border="1" |- ! Name ! Inequality |- | Cauchy-Schwarz inequality | For <mat...")
- 16:26, 7 March 2015 (diff | hist) . . (+25) . . m Main Page
- 16:18, 7 March 2015 (diff | hist) . . (+367) . . m Norm
- 16:13, 7 March 2015 (diff | hist) . . (+116) . . Norm (Missed 4th property)
- 16:12, 7 March 2015 (diff | hist) . . (0) . . m Metric space
- 16:11, 7 March 2015 (diff | hist) . . (0) . . m Triangle inequality (Alec moved page Triangle Inequality to Triangle inequality without leaving a redirect: To keep with naming conventions)
- 16:08, 7 March 2015 (diff | hist) . . (+557) . . N Absolute value (Created page with "The absolute value is sometimes called "abs" ==Definition== The absolute value is a function <math>|\cdot|:\mathbb{R}\rightarrow\mathbb{R}</math> given by: <mat...")
- 16:07, 7 March 2015 (diff | hist) . . (+21) . . N Category:Real Analysis (Created page with "Category:Subjects") (current)
- 16:06, 7 March 2015 (diff | hist) . . (+26) . . N Category:Real Analysis Definitions (Created page with "Category:Real Analysis") (current)
- 16:04, 7 March 2015 (diff | hist) . . (+386) . . N Norm (Created page with "==Definition== A norm on a vector space {{M|(V,F)}} is a function <math>\|\cdot\|:V\rightarrow\mathbb{R}</math> such that: # <math>\forall x\in V\ \|x\|\ge 0<...")
- 15:54, 7 March 2015 (diff | hist) . . (+572) . . N Example comparing bilinear to linear maps (Created page with "==Addition is a linear map== Here we will show that addition, given by:<br/> Take {{M|T:\mathbb{R}\rightarrow\mathbb{R} }} with <math>T(x)=x+x</math><br /> is a Linear map|l...")
- 15:50, 7 March 2015 (diff | hist) . . (+21) . . N Category:Linear Algebra Examples (Created page with "Category:Examples") (current)
- 15:50, 7 March 2015 (diff | hist) . . (+122) . . N Category:Examples (Created page with "This is a category where examples ought to be. To add use something like: <pre> {{Example|Topology|Linear Algebra}} </pre>") (current)
- 15:48, 7 March 2015 (diff | hist) . . (+244) . . N Template:Example (Created page with "<includeonly> Category:Examples {{#if: {{{1|}}} | [[Category:{{{1}}} Examples]] | }} {{#if: {{{1|}}} | [[Category:{{{1}}}]] | }} {{#if: {{{2|}}} | Category:{{{2}}} Examp...") (current)
- 15:47, 7 March 2015 (diff | hist) . . (+60) . . m Linear map
- 15:34, 7 March 2015 (diff | hist) . . (+422) . . m Linear map
- 15:29, 7 March 2015 (diff | hist) . . (+1,370) . . N Bilinear map (Created page with "A bilinear map combines elements from 2 vector spaces to yield and element in a third (in contrast to a linear map which takes a point in a vec...")
- 15:14, 7 March 2015 (diff | hist) . . (+11) . . m Vector space
- 15:12, 7 March 2015 (diff | hist) . . (+73) . . m Vector space
- 15:10, 7 March 2015 (diff | hist) . . (+251) . . m Vector space
- 15:09, 7 March 2015 (diff | hist) . . (+637) . . N Linear map (Created page with "==Definition== Given two vector spaces {{M|(U,F)}} and {{M|(V,F)}} (it is important that they are over the same field) we say that a map, <math>T:(U,F)\righta...")
- 15:04, 7 March 2015 (diff | hist) . . (+1,682) . . m Vector space
- 13:51, 6 March 2015 (diff | hist) . . (+698) . . N Equivalence relation (Created page with "An equivalence relation is a special kind of relation ==Required properties== Given a relation {{M|R}} in {{M|A}} we require the following properties to define a...")
- 16:42, 5 March 2015 (diff | hist) . . (+128) . . m Relation
- 16:40, 5 March 2015 (diff | hist) . . (+934) . . m Relation
- 15:43, 5 March 2015 (diff | hist) . . (+1,694) . . N Ordering (Created page with "An ordering is a special kind of relation, other than the concept of a relation we require three properties before we can define it. ==Required properties== Thes...")
- 01:25, 5 March 2015 (diff | hist) . . (+1) . . m Todo list
- 01:24, 5 March 2015 (diff | hist) . . (+90) . . m Todo list
- 01:22, 5 March 2015 (diff | hist) . . (+103) . . N Todo list (Created page with "* Proof that a function is invertible iff it is one to one (Jech, Set Theory - p 25) {{Todo|Do these}}")
- 22:24, 4 March 2015 (diff | hist) . . (+336) . . N The domain, range and field of a relation exist (Created page with "It is important to know that the domain and range of a relation exist. ==Proof that domain exists== We are given a relation {{M|R}} and wish to show the set <mat...")
- 22:21, 4 March 2015 (diff | hist) . . (+111) . . m Relation
- 22:19, 4 March 2015 (diff | hist) . . (+605) . . N Ordered pair (Created page with "An ordered pair <math>(a,b)=\{\{a\},\{a,b\}\}</math>, this way <math>(a,b)\ne(b,a)</math>. Ordered pairs are vital in the study of relations which leads to Fun...")
- 22:18, 4 March 2015 (diff | hist) . . (+646) . . m Set theory axioms
- 22:04, 4 March 2015 (diff | hist) . . (+663) . . m Set theory axioms
- 22:27, 1 March 2015 (diff | hist) . . (+113) . . N Editing guide (Created page with "==Maths== To get maths (LaTeX) use: <pre> <math>Maths here</math> [math]Maths here[/math] {{M|Maths here}} </pre>")
- 22:23, 1 March 2015 (diff | hist) . . (+38) . . m Main Page
- 22:22, 1 March 2015 (diff | hist) . . (+101) . . N Category:Theorems, lemmas and corollaries (Created page with "This is for all theorems, lemmas, propositions, remarks, so forth. The templates should include them.") (current)
- 22:19, 1 March 2015 (diff | hist) . . (+286) . . N Template:Lemma (Created page with "<includeonly> Category:Theorems Category:Theorems, lemmas and corollaries {{#if: {{{1|}}} | [[Category:{{{1}}} Lemmas]] | }} {{#if: {{{1|}}} | [[Category:{{{1}}}]] | }...") (current)
- 22:14, 1 March 2015 (diff | hist) . . (+46) . . m Template:Theorem Of
- 22:12, 1 March 2015 (diff | hist) . . (+185) . . m Relation
- 22:07, 1 March 2015 (diff | hist) . . (+369) . . m Relation
- 18:40, 1 March 2015 (diff | hist) . . (+779) . . N Relation (Created page with "A set {{M|R}} is a binary relation if all elements of {{M|R}} are ordered pairs. That is for any {{M|z\in R\ \exists x\text{ and }y:(x,y)}} ==Notation== Rat...")
- 00:25, 1 March 2015 (diff | hist) . . (+16) . . m Tuple
- 23:11, 28 February 2015 (diff | hist) . . (+515) . . N Implies (Created page with "The implies relation, denoted <math>A\implies B</math> or <math>B\impliedby A</math> where {{M|A\text{ and }B}} are statements of some sort means: {| class="wikitable" border...")
- 23:06, 28 February 2015 (diff | hist) . . (+57) . . m Set theory axioms
- 23:03, 28 February 2015 (diff | hist) . . (+7) . . m Motivation for set theory axioms (current)
- 23:01, 28 February 2015 (diff | hist) . . (+3,052) . . N Motivation for set theory axioms (Created page with "This assumes you have some "general idea" of what a set is. For example you are happy that {{M|\{1,2,3\}=\{2,1,3\} }} and that this set (I use singular because they are identi...")
- 22:20, 28 February 2015 (diff | hist) . . (+98) . . N Category:Subjects (Created page with "This category should contain the distinct subject '''categories''' on this wiki, not actual pages.") (current)
- 22:15, 28 February 2015 (diff | hist) . . (+21) . . N Category:Set Theory (Created page with "Category:Subjects") (current)
- 22:07, 28 February 2015 (diff | hist) . . (+849) . . N Set theory axioms (Created page with "This page is supposed to provide some discussion for the axioms (for example "there exists a set with no elements" doesn't really deserve its own page) ==List of axioms== The...")
- 20:01, 28 February 2015 (diff | hist) . . (+31) . . m Function
- 19:57, 28 February 2015 (diff | hist) . . (+989) . . N Function (Created page with "A function {{M|f}} is a special kind of relation ==Domain== A function '''ought''' be defined for everything in its domain, that's for every point in the domain...")
- 16:51, 28 February 2015 (diff | hist) . . (+153) . . m Main Page
- 12:38, 28 February 2015 (diff | hist) . . (+48) . . N Category:Set Theory Definitions (Created page with "Category:Set Theory Category:Definitions") (current)
- 12:34, 28 February 2015 (diff | hist) . . (+23) . . N Category:Linear Algebra (Created page with "Linear Algebra category")
- 12:31, 28 February 2015 (diff | hist) . . (+52) . . N Category:Linear Algebra Definitions (Created page with "Category:Definitions Category:Linear Algebra")
- 12:27, 28 February 2015 (diff | hist) . . (+21) . . N Category:Metric Space (Created page with "Category:Topology") (current)
- 12:26, 28 February 2015 (diff | hist) . . (+50) . . N Category:Metric Space Definitions (Created page with "Category:Definitions Category:Metric Space") (current)
- 12:22, 28 February 2015 (diff | hist) . . (+52) . . N Category:Measure Theory Definitions (Created page with "Category:Measure Theory Category:Definitions") (current)
- 12:20, 28 February 2015 (diff | hist) . . (+45) . . N Category:Set Theory Theorems (Created page with "Category:Theorems Category:Set Theory")
- 12:19, 28 February 2015 (diff | hist) . . (+17) . . N Category:Theorems (Created page with "Theorems category") (current)
- 12:12, 28 February 2015 (diff | hist) . . (+66) . . N Category:Topology Theorems (Created page with "Topology theorems here Category:Topology Category:Theorems") (current)
- 12:06, 28 February 2015 (diff | hist) . . (+23) . . N Category:Measure Theory (Created page with "Measure Theory category") (current)
- 19:28, 27 February 2015 (diff | hist) . . (+594) . . N Tuple (Created page with "==Definition== A tuple is a (potentially) mixed type vector of things. However as it may not be in a vector space we do not call it a vector. ==Examples== <m...")
- 19:21, 27 February 2015 (diff | hist) . . (+650) . . N Product topology (Created page with "Given a set {{M|X_{\alpha\in I} }} of indexed topological spaces, we define the product topology, denoted <math>\prod_{\alpha\in I}X_\al...")
- 19:10, 27 February 2015 (diff | hist) . . (0) . . m Homeomorphism
- 19:09, 27 February 2015 (diff | hist) . . (0) . . m Bijection
- 19:07, 27 February 2015 (diff | hist) . . (+1,259) . . m Topology
- 19:05, 27 February 2015 (diff | hist) . . (0) . . m Power set (Alec moved page Power Set to Power set without leaving a redirect)
- 18:45, 27 February 2015 (diff | hist) . . (+849) . . m Topology
- 16:01, 27 February 2015 (diff | hist) . . (+27) . . m Triangle inequality
- 16:00, 27 February 2015 (diff | hist) . . (+1,184) . . N Triangle inequality (Created page with "The triangle inequality takes a few common forms {{M||d(x,z)\le d(x,y)+d(y,z)}} of which <math>|x-z|\le|x-y|+|y-z|</math> is a special case. Another common way of writing it...")
- 07:35, 17 February 2015 (diff | hist) . . (+586) . . N Measure space (Created page with "Before we can define Measure space we need a measurable space. ==Measurable Space== Let {{M|X}} be a set and {{M|\mathcal{A} }} a \sigma}}-algebra, then...")
- 00:26, 17 February 2015 (diff | hist) . . (+31) . . m Limit point
- 00:25, 17 February 2015 (diff | hist) . . (+1,166) . . N Closure, interior and boundary (Created page with "These three things have their own page because of how often they come together. ==Closure== The closure of a set {{M|A}} denoted {{M|\bar{A} }} ("bar" in LaTeX) or {{M|\overl...")
- 23:53, 16 February 2015 (diff | hist) . . (+35) . . N Category:Topology (Created page with "All things to do with Topology here") (current)
- 23:51, 16 February 2015 (diff | hist) . . (+312) . . N The set of all open balls of a metric space are able to generate a topology and are a basis for that topology (Created page with "For a metric space {{M|(X,d)}} there is a topology which the metric induces on {{M|x}} that is the topology of all sets which are Open...")
- 07:27, 16 February 2015 (diff | hist) . . (+8) . . N Vector space (Created page with "{{Todo}}")
- 05:49, 15 February 2015 (diff | hist) . . (+1) . . m Continuous map
- 05:47, 15 February 2015 (diff | hist) . . (+385) . . N Homomorphism (Created page with "A Homomorphism '''(not to be confused with homeomorphism)''' is a structure preserving map. For example, given vector spaces {{M|V\text{ and }W}} then <math...")
- 05:43, 15 February 2015 (diff | hist) . . (+370) . . m Dual vector space
- 05:34, 15 February 2015 (diff | hist) . . (+9) . . m Dual vector space
- 05:30, 15 February 2015 (diff | hist) . . (+661) . . N Covering (Created page with " ==Definition== A covering of a set {{m|A}} is a collection {{m|\mathcal{A} }} where <math>A\subset\cup_{S\in\mathcal{A}}S</math>, that is as you'd expect, a collection of se...")
- 05:23, 15 February 2015 (diff | hist) . . (-5) . . m Compactness
- 05:22, 15 February 2015 (diff | hist) . . (+582) . . m Compactness
- 05:07, 15 February 2015 (diff | hist) . . (+321) . . m Subspace topology
- 05:07, 15 February 2015 (diff | hist) . . (-3) . . m Template:M
- 04:57, 15 February 2015 (diff | hist) . . (-21) . . m Closed set
- 04:56, 15 February 2015 (diff | hist) . . (-34) . . m Template:M
- 04:55, 15 February 2015 (diff | hist) . . (+34) . . m Template:M
- 04:54, 15 February 2015 (diff | hist) . . (-41) . . m Template:M
- 04:53, 15 February 2015 (diff | hist) . . (+82) . . m Closed set
- 04:49, 15 February 2015 (diff | hist) . . (+167) . . N Closed set (Created page with "A closed set in a topological space <math>(X,\mathcal{J})</math> is a set <math>A</math> where <math>X-A</math> is open. {{Definition|Topology}}")
- 04:47, 15 February 2015 (diff | hist) . . (+748) . . m Compactness
- 19:54, 14 February 2015 (diff | hist) . . (-9) . . m Commutativity of intersection
- 19:53, 14 February 2015 (diff | hist) . . (+555) . . m Commutativity of intersection
- 19:47, 14 February 2015 (diff | hist) . . (+476) . . m Connected (topology)
- 00:32, 14 February 2015 (diff | hist) . . (+16) . . m Surjection
- 19:27, 13 February 2015 (diff | hist) . . (+1) . . m Compactness
- 18:51, 13 February 2015 (diff | hist) . . (+61) . . N Commutativity of intersection (Created page with "<math>A\cap B=B\cap A</math> {{Todo}} {{Theorem|Set Theory}}")
- 18:46, 13 February 2015 (diff | hist) . . (+281) . . m The relationship between logical implication and the subset relation
- 18:42, 13 February 2015 (diff | hist) . . (+3) . . m The relationship between logical implication and the subset relation
- 18:37, 13 February 2015 (diff | hist) . . (+15) . . m Compactness
- 18:35, 13 February 2015 (diff | hist) . . (0) . . m Nabla (current)
- 18:30, 13 February 2015 (diff | hist) . . (-1) . . m Nabla
- 18:14, 13 February 2015 (diff | hist) . . (+117) . . m The intersection of sets is a subset of each set
- 18:13, 13 February 2015 (diff | hist) . . (+550) . . N The intersection of sets is a subset of each set (Created page with "==Theorem== That <math>A\cap B\subset A</math> Of course by commutivity of <math>\cap</math> we have <math>A\cap B\subset B</math> (as <math>...")
- 18:07, 13 February 2015 (diff | hist) . . (+1,470) . . m Compactness
- 17:45, 13 February 2015 (diff | hist) . . (0) . . m Compactness
- 17:44, 13 February 2015 (diff | hist) . . (+718) . . m Compactness
- 17:37, 13 February 2015 (diff | hist) . . (+49) . . m Compactness
- 17:35, 13 February 2015 (diff | hist) . . (+371) . . m Compactness
- 16:21, 13 February 2015 (diff | hist) . . (+177) . . m Topology
- 16:19, 13 February 2015 (diff | hist) . . (+101) . . N The relationship between logical implication and the subset relation (Created page with "The relation states that <math>[A\subset B]\iff[x\in A\implies x\in B]</math> {{Theorem|Set Theory}}")
- 16:17, 13 February 2015 (diff | hist) . . (+253) . . m Continuity definitions are equivalent
- 16:13, 13 February 2015 (diff | hist) . . (+2,110) . . m Continuity definitions are equivalent
- 15:47, 13 February 2015 (diff | hist) . . (+23) . . m Continuity definitions are equivalent
- 15:46, 13 February 2015 (diff | hist) . . (+2) . . m Template:Definition
- 15:45, 13 February 2015 (diff | hist) . . (+244) . . N Template:Theorem Of (Created page with "<includeonly> Category:Theorems {{#if: {{{1|}}} | [[Category:{{{1}}} Theorems]] | }} {{#if: {{{1|}}} | [[Category:{{{1}}}]] | }} {{#if: {{{2|}}} | Category:{{{2}}} Theor...")
- 15:41, 13 February 2015 (diff | hist) . . (-15) . . m Continuous map
- 15:40, 13 February 2015 (diff | hist) . . (+90) . . N Continuity definitions are equivalent (Created page with "{{Todo|Theorem B16 in Introduction to topological manifolds is a good guide to structure}}")
- 15:39, 13 February 2015 (diff | hist) . . (+1,364) . . N Motivation for topology (Created page with "This is the most important thing on this Wiki probably, the motivation for topology. Recall the definition of continuity, on a [[Metric space|metric space]...") (current)
- 14:51, 13 February 2015 (diff | hist) . . (+439) . . N Quotient topology (Created page with "==Definition== If <math>(X,\mathcal{J})</math> is a topological space, <math>A</math> is a set, and <math>p:(X,\mathcal{J})\rightarrow A</math> is a Su...")
- 14:34, 13 February 2015 (diff | hist) . . (+453) . . N Subspace topology (Created page with " ==Definition== We define the subspace topology as follows. Given a topological space <math>(X,\mathcal{J})</math> and any <math>Y\subset X</math> we ca...")
- 14:23, 13 February 2015 (diff | hist) . . (+330) . . N Compactness (Created page with " ==Definition== A topological space is compact if every open cover (often denoted <math>\mathcal{A}</math>) of <math>X</math> contains...")
- 14:09, 13 February 2015 (diff | hist) . . (+230) . . m Connected (topology)
- 14:06, 13 February 2015 (diff | hist) . . (+18) . . m Open set
- 14:04, 13 February 2015 (diff | hist) . . (+127) . . m Open set
- 14:03, 13 February 2015 (diff | hist) . . (+433) . . N Connected (topology) (Created page with " ==Definition== A topological space <math>(X,\mathcal{J})</math> is connected if there is no separation of <math>X</math> ===Separation=== This belongs...")
- 13:55, 13 February 2015 (diff | hist) . . (+31) . . m Dual vector space
- 13:31, 13 February 2015 (diff | hist) . . (+168) . . N Dual vector space (Created page with "Here a vector space is denoted as <math>(V,K)</math> where <math>K</math> is the field the vector space is over. The Dual space <math>V^*</math> is defined as follows:")
- 00:53, 13 February 2015 (diff | hist) . . (+143) . . N Surjection (Created page with "Surjective is onto - for <math>f:A\rightarrow B</math> every element of <math>B</math> is mapped onto from at least one thing in <math>A</math>")
- 00:43, 13 February 2015 (diff | hist) . . (-2) . . m Template:Definition
- 00:35, 13 February 2015 (diff | hist) . . (+37) . . m Limit point
- 00:28, 13 February 2015 (diff | hist) . . (+1,380) . . N Continuous map (Created page with "{{Definition|Topology|Metric Space}} ==First form== The first form: <math>f:A\rightarrow B</math> is continuous at <math>a</math> if:<br /> <math>\forall\epsilon>0\exists\de...")
- 23:57, 12 February 2015 (diff | hist) . . (+25) . . m Main Page
- 23:56, 12 February 2015 (diff | hist) . . (+1,471) . . N Nabla (Created page with "{{Definition}} ==Definition== <math>\nabla(\ )=\mathbf{i}\frac{\partial(\ )}{\partial x}+\mathbf{j}\frac{\partial(\ )}{\partial y}+\mathbf{k}\frac{\partial(\ )}{\partial z}</...")
- 22:35, 12 February 2015 (diff | hist) . . (0) . . m Metric space (Silly error)
- 21:15, 12 February 2015 (diff | hist) . . (+794) . . N Limit point (Created page with "{{Definition|Topology|Metric Space}} ==Definition== ===Common form=== For a Topological space <math>(X,\mathcal{J})</math>, <math>x\in X</math> is a limit point of <math>...")
- 21:14, 12 February 2015 (diff | hist) . . (+44) . . m Metric space
- 20:57, 12 February 2015 (diff | hist) . . (0) . . m Topological space (Alec moved page Topological Space to Topological space without leaving a redirect)
- 20:51, 12 February 2015 (diff | hist) . . (+30) . . m Open ball
- 20:46, 12 February 2015 (diff | hist) . . (+1,334) . . N Metric space (Created page with " ==Definition of a metric space== A metric space is a set <math>X</math> coupled with a "distance function" <math>d:X\times X\rightarrow\mathbb{R}</math> with the properties...")
- 20:28, 12 February 2015 (diff | hist) . . (+87) . . N Category:Todo (Created page with "Use the "Todo" (with an optional message) template to register things in this category.")
- 20:27, 12 February 2015 (diff | hist) . . (+508) . . N Open ball (Created page with "{{Definition|Topology|Metric Space}} For a metric space <math>(X,d)</math> an "open ball" of radius <math>r</math> centred at <math>a</math> is the set <math...")
- 19:54, 12 February 2015 (diff | hist) . . (+44) . . m Main Page
- 19:53, 12 February 2015 (diff | hist) . . (+71) . . N Template:Todo (Created page with "<includeonly> ---- TODO: {{{1|}}} Category:Todo ---- </includeonly>")
- 19:30, 12 February 2015 (diff | hist) . . (+566) . . N Open set (Created page with "{{Definition|Topology|Metric Space}} Here <math>(X,d)</math> denotes a metric space, and <math>B_r(x)</math> the open ball centred at <math>x</math> of radius <...")
- 19:07, 12 February 2015 (diff | hist) . . (+920) . . N Topological space (Created page with "A topological space is a set <math>X</math> coupled with a topology on <math>X</math> denoted <math>\mathcal{J}\subset\mathcal{P}(X)</math>, which is a collection of subsets o...")
- 18:58, 12 February 2015 (diff | hist) . . (+88) . . m Template:Definition
- 18:56, 12 February 2015 (diff | hist) . . (+44) . . m Category:Topology Definitions
- 18:55, 12 February 2015 (diff | hist) . . (+666) . . N Injection (Created page with "An injective function is 1:1, but not nessasarally onto. For <math>f:X\rightarrow Y</math> every element of <math>X</math> is mapped to an element of <math>Y</...")
- 18:48, 12 February 2015 (diff | hist) . . (+42) . . N Category:Definitions (Created page with "This includes all definitions on the site.")
- 18:48, 12 February 2015 (diff | hist) . . (+7) . . m Power set
- 18:46, 12 February 2015 (diff | hist) . . (+28) . . m Template:M
- 18:37, 12 February 2015 (diff | hist) . . (-26) . . m Template:M
- 18:34, 12 February 2015 (diff | hist) . . (+10) . . m Template:M
- 18:34, 12 February 2015 (diff | hist) . . (-24) . . m Template:M
- 18:33, 12 February 2015 (diff | hist) . . (+52) . . m Template:M
- 18:29, 12 February 2015 (diff | hist) . . (-27) . . m Template:M
- 18:25, 12 February 2015 (diff | hist) . . (+29) . . m Template:M
- 18:16, 12 February 2015 (diff | hist) . . (0) . . m Template:M
- 18:15, 12 February 2015 (diff | hist) . . (+22) . . m Template:M
- 18:13, 12 February 2015 (diff | hist) . . (+9) . . m Power set
- 18:13, 12 February 2015 (diff | hist) . . (+50) . . N Template:M (Helper template)
- 18:09, 12 February 2015 (diff | hist) . . (+8) . . m Homeomorphism
- 18:07, 12 February 2015 (diff | hist) . . (+16) . . Bijection
- 18:06, 12 February 2015 (diff | hist) . . (-2) . . Template:Definition
- 18:06, 12 February 2015 (diff | hist) . . (+2) . . Template:Definition
- 18:05, 12 February 2015 (diff | hist) . . (0) . . Template:Definition
- 18:04, 12 February 2015 (diff | hist) . . (0) . . Template:Definition
- 18:01, 12 February 2015 (diff | hist) . . (+2) . . Template:Definition
- 17:59, 12 February 2015 (diff | hist) . . (-11) . . Homeomorphism
- 17:58, 12 February 2015 (diff | hist) . . (+29) . . Template:Definition
- 17:56, 12 February 2015 (diff | hist) . . (+134) . . N Template:Definition (Created page with "Category:Definitions {{#if {{{1}}} | [[Category::{{{1}}} Definitions]] | }} {{#if {{{2}}} | [[Category::{{{2}}} Definitions]] | }}")
- 17:50, 12 February 2015 (diff | hist) . . (+24) . . N Category:Topology Definitions (Created page with "Category:Definitions")
- 17:50, 12 February 2015 (diff | hist) . . (+36) . . Homeomorphism
- 17:47, 12 February 2015 (diff | hist) . . (+476) . . N Power set (Created page with "The power set of a set <math>X</math> is denoted by <math>\mathcal{P}(X)</math>, sometimes <math>2^X</math> (a number to the power of a set is not defined (as it cannot be use...")
- 17:43, 12 February 2015 (diff | hist) . . (+481) . . N Bijection (Created page with "A bijection is a 1:1 map. A map which is both injective and surjective. It has the useful property that for <math>f:X\rightarrow Y</math> that <...")
- 17:37, 12 February 2015 (diff | hist) . . (+388) . . N Homeomorphism (Created page with "Not to be confused with "Homomorphism" ==Topological Homeomorphism== A topological homeomorphism is bijective map between two Topological Space|topological s...")
- 17:31, 12 February 2015 (diff | hist) . . (+58) . . N Topology (Created page with "This is the root page for Topology. Category:Topology")
- 17:28, 12 February 2015 (diff | hist) . . (+13) . . Main Page
- 17:23, 12 February 2015 (diff | hist) . . (-528) . . Main Page
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