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Difference between revisions of "Deformation retract"

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(Category:Algebraic topology)
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''of a topological space $X$''
 
''of a topological space $X$''
  
A subset $A\subset X$ with the following property: There exists a homotopy of the identity mapping of $X$ to some mapping $X\to A$ under which all points of the set $A$ remain fixed. If, under the homotopy, the points from $X\setminus A$ remain in $X\setminus A$, $A$ is known as a strong deformation retract. A deformation retract of a space $X$ has the same [[homotopy type]] as does $X$. See also [[Retract]]; [[Retract of a topological space]].
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A subset $A\subset X$ with the following property: There exists a [[homotopy]] of the identity mapping of $X \to X$ to some mapping $X\to A$ under which all points of the set $A$ remain fixed. If, under the homotopy, the points from $X\setminus A$ remain in $X\setminus A$, $A$ is known as a strong deformation retract. A deformation retract of a space $X$ has the same [[homotopy type]] as does $X$. See also [[Retract]]; [[Retract of a topological space]].
  
 
[[Category:Algebraic topology]]
 
[[Category:Algebraic topology]]

Latest revision as of 19:45, 5 February 2016

of a topological space $X$

A subset $A\subset X$ with the following property: There exists a homotopy of the identity mapping of $X \to X$ to some mapping $X\to A$ under which all points of the set $A$ remain fixed. If, under the homotopy, the points from $X\setminus A$ remain in $X\setminus A$, $A$ is known as a strong deformation retract. A deformation retract of a space $X$ has the same homotopy type as does $X$. See also Retract; Retract of a topological space.

How to Cite This Entry:
Deformation retract. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Deformation_retract&oldid=37658
This article was adapted from an original article by E.G. Sklyarenko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article