Open map

An open map sends every open subset of its source to an open subset of its target. This is an image property; continuity instead concerns preimages of open sets. A local diffeomorphism has both properties, but openness alone does not promise unique recovery of an input. In the periodic coordinate map under the inverse function theorem, open patches give open output regions while multiple angle values still give the same output.

Together, open and closed maps describe the two image-set preservation properties.