Definition:Retraction (Topology)

Definition
Let $T_1 = \struct {S_1, \tau_1}$ be a topological space.

Let $T_2 = \struct {S_2, \tau_2}$ be a topological subspace of $T_1$.

That is:
 * $S_2 \subseteq S_1$

Let $f: S_1 \to S_2$ be a mapping.

Then $f$ is retraction of $T_1$
 * $\forall s \in S_2: \map f s = s$

Also see

 * Definition:Retract (Topology)