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.