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• Homotopy
  ...Alec|Alec]] ([[User talk:Alec|talk]]) 19:31, 26 November 2017 (UTC) |grade=A}} {{Requires references|grade=A}}
  3 KB (512 words) - 19:31, 26 November 2017
• The stages of a homotopy are continuous
  ...M|1=I:=[0,1]\subset\mathbb{R} }}), the [[stage of a homotopy|stages of the homotopy {{M|F}}]] are [[continuous]]<ref>Alec's own work</ref>. More concisely: * For a [[homotopy]], {{M|F:X\times I\rightarrow Y}}, for all {{M|t\in I}} the map {{M|f_t:X\r
  974 B (168 words) - 23:46, 2 May 2016
• Homotopic maps
  ...grade=A*|msg=Needs fleshing out, more references. Made a bit of a mess out of it, but I'll leave tidying up until later!}} ...s]]'' [[map|maps]] and let {{M|A\in\mathcal{P}(X)}} be an arbitrary subset of {{M|X}}.
  4 KB (674 words) - 13:26, 15 September 2016
• Homotopy (object)
  {{Stub page|grade=A}} {{Requires references|grade=A}}
  2 KB (296 words) - 04:25, 1 July 2016
• HomotopyPage
  ...|F:X\times I\rightarrow Y}}, we get homotopic maps. So a homotopy warrants a definition, even if it is useless by itself. ...l{P}(X)}} be an arbitrary subset of {{M|X}}. A ''homotopy, relative to {{M|A}}'' is, in its purest form, is any ''[[continuous]]'' [[map]]:
  2 KB (401 words) - 12:53, 15 September 2016
• Notes:Homotopy terminology/Terminology
  ...t of {{M|X}}. Let {{M|C^0(X,Y)}} denote the set of all [[continuous maps]] of the form {{M|(:X\rightarrow Y)}}. Let {{M|1=I:=[0,1]:=\{x\in\mathbb{R}\ \ve ...I\rightarrow Y}} such that: {{M|1=\forall a\in A\forall s,t\in I[H(a,t)=H(a,s)]}}.
  900 B (184 words) - 14:40, 16 September 2016
• Homotopy is an equivalence relation on the set of all continuous maps between spaces/proof
  ...relation]] we must show:{{M|\newcommand{\homo}[2]{#1\simeq #2\ (\text{rel }A)} }} # For all {{M|f\in C^0(X,Y)}} that {{M|f\simeq f\ (\text{rel }A)}}, symbolically:
  3 KB (533 words) - 07:33, 18 September 2016
• Doctrine:Homotopy terminology
  * Let {{M|A\in\mathcal{P}(X)}} be an [[arbitrary subset]] of {{M|X}} ...group="Note">The 0 comes from this being notation being used for [[classes of continuously differentiable functions]], {{M|C^1}} means all continuous fun
  3 KB (535 words) - 09:01, 31 October 2016
• Homotopy concatenation
  {{Stub page|grade=A|msg=Typical stub page}} ...0)]}} - that the final stage of {{M|H_1}} is the same as the initial stage of {{M|H_2}}
  2 KB (260 words) - 05:09, 6 November 2016
• The composition of end-point-preserving-homotopic paths with a continuous map yields end-point-preserving-homotopic paths
  ...{Top.|Y|K}} be [[topological spaces]], let {{M|\varphi:X\rightarrow Y}} be a [[continuous map]] and let {{M|f_1,f_2:I\rightarrow X}} be {{link|path|topo * The relation of paths being end-point-preseriving-homotopic is preserved under [[function c
  2 KB (282 words) - 22:38, 12 December 2016
• Evenly covered by a continuous map
  {{Stub page|grade=A**|msg=find another source! I have encountered many variations}} {{Provisional page|grade=A*|msg=Books conflict on whether or not the {{M|V_\alpha}} must be connected.
  2 KB (394 words) - 21:54, 24 February 2017