# Deformation retract

From Encyclopedia of Mathematics

*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