# Definition:Closed Mapping

## Definition

Let $X, Y$ be topological spaces.

Let $f : X \to Y$ be 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

- Results about
**closed mappings**can be found here.

## Sources

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