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

• Results about open 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