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

Revision as of 15:53, 10 July 2014

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 $x\in A$.


Comments

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=32408
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article