Deformation retraction
= Deformation retraction
{wiki=Retraction_(topology)#Deformation_retract_and_strong_deformation_retract}
A deformation retraction of $X$ onto $A$ is a homotopy from $\operatorname{id}_X$ to a retraction $r:X\to A$ that keeps $A$ inside itself throughout. It makes the inclusion $A\hookrightarrow X$ a <homotopy equivalence>.