User contributions
From Maths
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- 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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