Definition:Retract (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 $T_1$.

Then $T_2$ is a retract of $T_1$ if and only if

there exists a continuous retraction $f: S_1 \to S_2$ of $T_1$.

Absolute Retract

$T_2$ is an absolute retract of $T_1$ if and only if:

for every closed subspace $B$ of a $T_4$ space $T$ such that $B$ is homeomorphic to $A$, then $B$ is a retract of $T$.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): retract

• Mizar article BORSUK_1:def 17