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• Connected (topology)
  {{Refactor notice|grade=A|msg=Ancient page, needs an update, linking to theorems, so forth}} ...t be put off if you have found ''another'' definition! I have started with the most intuitive definition
  5 KB (866 words) - 01:52, 1 October 2016
• Topological property theorems
  ...ving topological properties, like [[Compactness|compactness]], [[Connected space|connectedness]], so forth. The a few types of theorems are (like):
  3 KB (616 words) - 08:37, 1 July 2015
• Exercises:Saul - Algebraic Topology - 3/Exercise 3.2
  ...Delta}}-complex]] structure. Show, directly from the definitions (Hatcher, of course...) that {{M|H^\Delta_0(X)\cong\mathbb{Z} }} * We may assume without proof that the {{M|1}}-skeleton is path connected.
  13 KB (2,312 words) - 06:33, 1 February 2017
• Intermediate value theorem
  ...e]] and suppose {{M|f:X\rightarrow}}[[the real line|{{M|\mathbb{R} }}]] is a [[continuous function]], then{{rITTMJML}}: ...that {{M|a\le b\le c}} really means {{M|(a\le b)\wedge(b\le c)}} - so {{M|a\le b}} ''and'' {{M|b\le c}}.</ref>
  5 KB (979 words) - 17:35, 17 February 2017
• Path-connected topological space
  {{Stub page|grade=A*|msg=Important to cover from multiple sources, demote after this. ...[n-torus]], {{M|\mathbb{T}^n}} is path connected as it is a finite product of [[circle|circles]]
  2 KB (249 words) - 12:52, 23 February 2017
• Exercises:Saul - Algebraic Topology - 7/Exercise 7.6
  ...ingular homology groups of {{M|T^2:\eq\mathbb{S}^1\times\mathbb{S}^1}} and of {{M|X:\eq\mathbb{S}^1\vee\mathbb{S}^1\vee\mathbb{S}^2}} ...gy groups of the {{M|2}}-torus have been computed in previous assignments, the result was:
  10 KB (1,664 words) - 12:43, 1 March 2017
• Unique lifting property
  ...each sheet is ''connected'' and disjoint from the others. Thus {{M|U}} is connected. It may not matter ...onnected neighbourhoods. It's worth investigating but it isn't critical to the theory.</ref>
  13 KB (2,510 words) - 16:23, 2 March 2017
• Exercises:Saul - Algebraic Topology - 9/Exercise 9.7
  ...}} {{M|C(\mathbb{RP}^2)}}, is not a [[topological n-manifold with boundary|topological 3-manifold with boundary]]. I might have two solutions for this, I accidentally answered the wrong question initially.
  8 KB (1,299 words) - 13:33, 15 March 2017