Definition:Retraction (Topology)

Definition
Let $T_1 = \left({S_1, \tau_1}\right)$ be a topological space.

Let $T_2 = \left({S_2, \tau_2}\right)$ be a topological subspace of $T_1$.

It means that
 * $S_2 \subseteq S_1$

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

Then $f$ is retraction of $T_1$
 * $\forall s \in S_2: f\left({s}\right) = s$

Also See

 * Definition:Retract (Topology)