Definition:Open Mapping

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

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

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