A subspace of is called a deformation retract of if there is a homotopy (called a retract) such that for all and ,
1. ,
2. , and
3. .
A tightening of the last condition gives a so-called strong deformation retract (Bredon 1993, pp. 45-46).
Note that a deformation retract is also a retract, because the homotopy defines a continuous map