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• Triangulations
  '''Theorem.''' A cell complex $K$ is a simplicial complex if for each of its cells $\t '''Theorem.''' $N_A$ is an open subset of $|K|$ for any vertex $A$ in $K$.
  30 KB (5,172 words) - 21:52, 26 November 2015
• Nerve of cover
  [[Image:nerve of circle.jpg|center]] [[Image:nerve example.jpg|center]]
  8 KB (1,389 words) - 13:35, 12 August 2015
• Topology Illustrated -- Index
  *[[Arrow's Impossibility Theorem|Arrow's Impossibility Theorem]] *[[Arzela-Ascoli Theorem|Arzela-Ascoli Theorem]]
  16 KB (1,773 words) - 00:41, 17 February 2016
• Homotopy
  '''Theorem.''' Homotopy is an equivalence relation. For two given topological spaces $ '''Theorem.''' Every map $f:[0,1]\to S$, where $S$ is a surface, is homotopic to a map
  46 KB (7,846 words) - 02:47, 30 November 2015
• Homotopy and homotopy equivalence
  '''Theorem.''' Homotopy is an equivalence relation. For two given topological spaces $ '''Theorem.''' Every map $f:[0,1]\to S$, where $S$ is a surface, is homotopic to a map
  45 KB (7,738 words) - 15:18, 24 October 2015
• Social choice
  '''Theorem.''' There is an algebraic mean of degree $m$ on an abelian group $G$ if and '''Theorem.''' Suppose $G$ is a free abelian group and suppose $f:G^m\to G$ is a symme
  47 KB (8,030 words) - 18:48, 30 November 2015
• Surfaces and their homology
  '''Theorem.''' The disjoint union of two surfaces is a surface. Because of this theorem we concentrate on ''[[connectedness|path-connected]] surfaces''. We will al
  17 KB (2,696 words) - 00:47, 12 January 2014
• Elections
  Therefore, the nerve of this cover will contain an edge between these two vertices. Then the spa '''Theorem.''' A rating tally satisfies Independence if and only if there is such a ho
  33 KB (5,872 words) - 13:13, 17 August 2015
• Test
  <TR> <TD><center>[[Stokes theorem]]</center></TD></TR> <TR> <TD><center>[[Image:Stokes theorem deconstructed.png|center]]</center></TD></TR>
  16 KB (2,139 words) - 23:01, 9 February 2015
• Applied Topology and Geometry
  <TR> <TD><center>[[Stokes theorem]]</center></TD></TR> <TR> <TD><center>[[Image:Stokes theorem deconstructed.png|center]]</center></TD></TR>
  16 KB (2,088 words) - 16:37, 29 November 2014
• Introductory algebraic topology: review exercises
  1. Can a discontinuous function satisfy the Intermediate Value Theorem? ...(b) Prove that a subspace of a Hausdorff space is Hausdorff. (c) State the theorem about homeomorphisms of Hausdorff spaces.
  9 KB (1,553 words) - 20:10, 23 October 2012
• The political spectrum is a circle
  <!--250-->[[image:political spectrum -- nerve D.png| center]] '''Impossibility Theorem.''' Suppose the graph of choices contains a topological circle. Then there
  8 KB (1,319 words) - 13:51, 10 August 2017
• Triangulations of surfaces
  ...ces is called the [[star of vertex]] $A$. For a related construction see [[Nerve of cover]]. '''Theorem.''' If a simplicial complex $K$ satisfies conditions (A) and (B) then its [
  3 KB (505 words) - 18:17, 27 August 2015