Definition:Open Mapping

Definition
Let $\left({X_1, \tau_1}\right)$ and $\left({X_2, \tau_2}\right)$ be topological spaces.

Let $f: X_1 \to X_2$ be a mapping.

Then $f$ is said to be an open mapping iff:
 * $\forall U \in \tau_1: f \left({U}\right) \in \tau_2$

where $f \left({U}\right)$ denotes the image of $U$ under $f$.

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

Also see

 * Closed mapping