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• Product and coproduct compared
  ...ory theory)|coproduct]] pages make it hard to see just how similar the two definitions are. As a result I shall steal the format from{{rAITCTHS2010}} and do a two ...pair {{M|A}}, {{M|B}} of [[object|objects]] in a [[category]] {{M|\mathscr{C} }} a:
  2 KB (351 words) - 16:59, 1 March 2016
• Site projects:Measure theory plan
  The plan is to stick pretty close to what Halmos does but introduce definitions found elsewhere, for example Measures, Integrals and Martingales introduces ! {{M|\mathcal{C} }}
  2 KB (309 words) - 15:31, 27 March 2016
• Notes:Types of retractions
  ==Definitions== * {{C|"The key is that if one want a continuous function r:X-->I ,then r can not
  6 KB (1,008 words) - 11:56, 2 June 2016
• Notes:Differential (manifolds)
  ==Definitions== * '''Smoothness of a map ({{AKA}}: {{M|C^\infty}}''' - a map, {{M|f:U\subseteq\mathbb{R}^n\rightarrow V\subseteq\mat
  4 KB (716 words) - 14:24, 16 May 2016
• Types of set algebras/Type table
  ...e that {{M|1=A-B=A\cap B^c=(A^c\cup B)^c}} - or that {{M|1=A-B=(A^c\cup B)^c}} - so we see that being closed under union and complement means we have cl ...under complements, so {{M|\emptyset^c\in\mathcal{A} }} and {{M|1=\emptyset^c=\Omega\in\mathcal{A} }}</ref>
  4 KB (573 words) - 20:00, 19 August 2016
• Editing guide/Templates/Page categorisation
  | To categorise definitions | {{C|<nowiki>{{Definition|</nowiki>Subject₁<nowiki>|...|Subject</nowi
  653 B (80 words) - 10:11, 8 September 2016
• Doctrine:Homotopy terminology
  Before we can define terms, here are the definitions we work with: ...ans continuous with continuous first and second derivatives, so forth, {{M|C^\infty}} means [[smooth]].
  3 KB (535 words) - 09:01, 31 October 2016
• Closed map
  * {{M|1=\forall U\in C(X,\mathcal{J})[f(U)\in C(Y,\mathcal{K})]}} - that is, that the {{link|image|map|s}} (under {{M|f}}) ** {{M|C(X,\mathcal{J})}} denotes the set of all {{plural|closed set|s}} of the [[to
  1 KB (246 words) - 19:59, 26 September 2016
• Every surjective map gives rise to an equivalence relation
  ...page|grade=C|msg=Flesh out, check existing content then demote to grade {{C|F}}}} ...2\in X[x_1\sim x_2\iff f(x_1)=f(x_2)]}} (for the "and only if" part, see [[definitions and iff]])
  2 KB (315 words) - 13:54, 8 October 2016
• Dense
  ...definitions to here, as they're like... "easy equivalent" and may well be definitions, not like ... a proposition of equivalence. ...p="Note">These are not just logically equivalent to density, they could be definitions for density, and may well be in some books.</ref>
  6 KB (1,097 words) - 04:15, 1 January 2017
• Notes:Homology
  ==Definitions== & & z \ar@/_.5pc/[uu]^c \ar@/_2pc/[uu]_d
  6 KB (897 words) - 07:30, 15 October 2016
• Invariant of an equivalence relation
  ...invariant of ''{{M|\sim}}" if<ref group="Note" name="definition">See "''[[definitions and iff]]''"</ref>: ...al{P}(S)}}, such that there [[exists a unique]] {{M|c\in C}} such that {{M|c\sim s}}
  3 KB (478 words) - 18:58, 9 November 2016
• Notes:Dual to dual vector space
  ** {{MM|A:v\mapsto\left(\begin{array}{c}:V^*\rightarrow\mathbb{F}\\:f^*\mapsto\ (???)\end{array}\right)}} in some w * After faffing about with the definitions and getting a "feel" for what was going on, I realised:
  2 KB (318 words) - 05:34, 8 December 2016
• List of topological properties
  ...)}} is a [[topological space]] or {{M|(X,d)}} is a [[metric space]] in the definitions. ...C}(X)\ \big\vert\ A\subseteq C\right\} }}{{rFAVIDMH}} - where {{M|\mathcal{C}(X)}} denotes the set of {{plural|closed set|s}} of {{M|X}}
  4 KB (630 words) - 19:33, 16 February 2017
• Index of notation for sets of continuous maps/Index
  ...C(X,Y)}}]] - for [[topological spaces]] {{Top.|X|J}} and {{Top.|Y|K}}, {{M|C(X,Y)}} is the [[set]] of all [[continuous maps]] between them. # [[C(I,X)|{{M|C(I,X)}}]] - {{M|I:\eq[0,1]\subset\mathbb{R} }}, set of all {{link|path|topol
  2 KB (463 words) - 06:20, 1 January 2017
• Exercises:Saul - Algebraic Topology - 3/Exercise 3.2
  ...[[Delta-complex|{{M|\Delta}}-complex]] structure. Show, directly from the definitions (Hatcher, of course...) that {{M|H^\Delta_0(X)\cong\mathbb{Z} }} ...the Abelian groups that usually have a {{M|C}} in them and how he used {{M|C}}.
  13 KB (2,312 words) - 06:33, 1 February 2017
• Doctrine:K
  : See also: [[Doctrine:Index]] for implicit definitions like these, conventions (like {{M|i}} for an index or {{M|f}} for a functio ...ither [[the reals|{{M|\mathbb{R} }}]] or [[the complex numbers|{{M|\mathbb{C} }}]]
  617 B (92 words) - 18:42, 16 February 2017
• Real projective space
  * Demote to grade C once charts and definition 1 is in place [[User:Alec|Alec]] ([[User talk:Al Let {{M|n\in\mathbb{N}_{\ge 1} }} be given. There are 2 common definitions for {{M|\mathbb{RP}^n}} that we encounter. We will use definition 1 unless
  2 KB (289 words) - 09:08, 18 February 2017
• Unique lifting property
  {{Requires work|grade=C|msg={{Warning|What follows is VERY messy.}} I was distracted when writing i Let us make the following definitions:
  13 KB (2,510 words) - 16:23, 2 March 2017
• Contractible topological space
  * {{M|\exists c\in X\big[(:x\mapsto c)\simeq \text{Id}_X\big]}} ...case {{M|(:X\rightarrow X)}} by {{M|(:x\mapsto c)}} for some constant {{M|c}}) that is [[homotopic maps|homotopic to]] {{M|\text{Id}_X:X\rightarrow X}}
  3 KB (544 words) - 20:00, 24 April 2017