Definition:Weak Retract (Topology)

Definition

Let $T_1 = \struct {S_1, \tau_1}$ and $T_2 = \struct {S_2, \tau_2}$ be topological spaces.

Then $T_1$ is a weak retract of $T_2$ if and only if there exists a continuous mapping $f: S_2 \to S_2$ such that:

$f \circ f = f$

and:

$\Img f$ and $T_1$ are homeomorphic.

Sources

• Mizar article WAYBEL18:def 8