Deformation retract

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of a topological space

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

How to Cite This Entry:
Deformation retract. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by E.G. Sklyarenko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article