Definition:Open Mapping

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

If, for any open set $U \subseteq X$, the image $f \left({U}\right)$ is open in $Y$, then $f$ is called open.

Note
This is not to be confused with the concept of $f$ being continuous.

Also see

 * Closed mapping