Closed map

A map $f : X \to Y$ between two topological spaces $(X, τ_{X})$ and $(Y, τ_{Y})$ is said to be closed if for any closed subset $C \subseteq X$ , the image $f (C) \subseteq Y$ is also closed in $Y$ .

In mathematical notation, $f$ is a closed map if for all closed $C \subseteq X$ , we have $f (C) \subseteq Y$ is closed:

\forall C \subseteq X, if C is closed in (X, τ_{X}), then f (C) is closed in (Y, τ_{Y}) .

This means that the inverse image of any closed set in $Y$ under $f$ is also closed in $X$ .