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Difference between revisions of "Retraction"

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A [[Continuous mapping|continuous mapping]] <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r081/r081700/r0817001.png" /> of a [[Topological space|topological space]] <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r081/r081700/r0817002.png" /> into a subspace <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r081/r081700/r0817003.png" /> which is the identity on <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r081/r081700/r0817004.png" />, i.e. is such that <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r081/r081700/r0817005.png" /> for all <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r081/r081700/r0817006.png" />.
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A [[continuous mapping]] $f$ of a [[topological space]] $X$ into a subspace $A$ which is the identity on $A$, ''i.e.'' is such that $f(x)=x$ for all $x\in A$.
  
 
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Cf. [[Retract of a topological space]] for more information and references.
 
 
====Comments====
 
Cf. [[Retract of a topological space|Retract of a topological space]] for more information and references.
 

Latest revision as of 14:02, 8 April 2023

A continuous mapping $f$ of a topological space $X$ into a subspace $A$ which is the identity on $A$, i.e. is such that $f(x)=x$ for all $x\in A$.

Cf. Retract of a topological space for more information and references.

How to Cite This Entry:
Retraction. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Retraction&oldid=11680
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article