Definition:Retraction (Topology)

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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 $T_1$ if and only if

$\forall s \in S_2: \map f s = s$


Also see


Sources