Definition:Closed Mapping

Definition

Let $X, Y$ be topological spaces and $f : X \to Y$ a mapping.

If, for any closed set $V \subseteq X$, the image $f \left({V}\right)$ is closed in $Y$, then $f$ is referred to as a closed mapping.

Also see

• Open mapping

• Results about closed mappings can be found here.

Sources

• Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (1970)... (previous)... (next): $\text{I}: \ \S 1$: Functions