retract

Definition

Let $X$ be a topological basis and $A\subset X$ be a subspace. A continuous map $r:X\to A$ is a retract if the restriction to $A$ is the identity map.

Written other ways,

$r{|}_A=i{d}_A$

or

$r\circ \iota =i{d}_A$

of finally

$r(a)=a\forall a\in A.$