# Definition:Open Mapping

## Definition

Let $\left({S_1, \tau_1}\right)$ and $\left({S_2, \tau_2}\right)$ be topological spaces.

Let $f: S_1 \to S_2$ be a mapping.

Then $f$ is said to be an open mapping if and only if:

$\forall U \in \tau_1: f \left[{U}\right] \in \tau_2$

where $f \left[{U}\right]$ denotes the image of $U$ under $f$.

## Warning

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

## Also see

• Results about open mappings can be found here.