= 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.
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