nLab
closed map

Definition

For maps between topological spaces

A function $f:X\to Y$ between topological spaces is called closed if the image of every closed set in $X$ is also closed in $Y$.

Recall that $f$ is a continuous map if the preimage of every closed set in $Y$ is closed in $X$. For defining closed maps typically one restricts attention to closed continuous maps, although it also makes sense to speak of closed functions that are not continuous.

See also open map (from which the above was blatantly adapted).