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• Homotopy
  <!--150-->[[image:circle homotopy type.png|center]] ...quivalence relation that produces the same result for a much broader class of spaces:
  46 KB (7,846 words) - 02:47, 30 November 2015
• Topology Illustrated -- Index
  *[[basis of neighborhoods|basis of neighborhoods]] *[[basis of topology|basis of topology]]
  16 KB (1,773 words) - 00:41, 17 February 2016
• Set-valued maps
  ==Coincidences of a pair of maps== ...question is, if $f:N\to M$ is a map, when can we guarantee that the image of $f$ is the whole $M$:
  24 KB (4,382 words) - 15:52, 30 November 2015
• Test
  [[Image:Tunnels_in_foam.png|200px|right|Complex 3d topology of a piece of foam]] A sample of the ideas that the text follows -- in broad brushstrokes.
  16 KB (2,139 words) - 23:01, 9 February 2015
• Applied Topology and Geometry
  [[Image:Tunnels_in_foam.png|200px|right|Complex 3d topology of a piece of foam]] A sample of the ideas that the text follows -- in broad brushstrokes.
  16 KB (2,088 words) - 16:37, 29 November 2014
• Fundamental group
  ..._1(X,x_{0})$, is the [[group]] of loops based at $x_{0}$, up to a based [[homotopy]]. We define a product on this group by where $<x>$ stands for the homotopy class of $x$ and $\sigma \cdot \tau$ means "travel along $\sigma$ and then $\tau$".
  10 KB (1,673 words) - 18:23, 2 December 2012
• Simply connected spaces
  [[Image:simply connected and independent of path.jpg|center]] ...ed ''simply connected'' if every closed curve can be "contracted" -- via [[homotopy]] -- to a point without leaving $X$:
  5 KB (785 words) - 22:07, 3 January 2014
• Axioms of chain complexes
  ...conditions on chain complexes guarantee the [[Eilenberg–Steenrod axioms]] of the homology they produce. Then these ''axioms'' become ''theorems'', prove In the Eilenberg–Steenrod axioms, the category of ''all'' pairs can be replaced with any subcategory ${\mathscr Top}$ as long
  4 KB (592 words) - 14:13, 4 August 2013
• Topology 2: course
  ...or advanced undergraduate and beginning graduate students. It is dependent of [[point set topology]]. *[[introductory calculus: course|calculus]] (parts of),
  1 KB (175 words) - 13:33, 17 March 2014