View source for Deformation retract

''of a topological space <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d030/d030730/d0307301.png" />''

A subset <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d030/d030730/d0307302.png" /> with the following property: There exists a homotopy of the identity mapping of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d030/d030730/d0307303.png" /> to some mapping <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d030/d030730/d0307304.png" /> under which all points of the set <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d030/d030730/d0307305.png" /> remain fixed. If, under the homotopy, the points from <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d030/d030730/d0307306.png" /> remain in <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d030/d030730/d0307307.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d030/d030730/d0307308.png" /> is known as a strong deformation retract. A deformation retract of a space <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d030/d030730/d0307309.png" /> has the same [[Homotopy type|homotopy type]] as does <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d030/d030730/d03073010.png" />. See also [[Retract|Retract]]; [[Retract of a topological space|Retract of a topological space]].