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 
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