[Merged by Bors] - feat(geometry/manifold/charted_space): open subset of a manifold is a manifold #3442
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Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr>
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… manifold (#3442) An open subset of a charted space is naturally a charted space. If the charted space has structure groupoid `G` (with `G` closed under restriction), then the open subset does also. Most of the work is in `topology/local_homeomorph`, where it is proved that a local homeomorphism whose source is `univ` is an open embedding, and conversely.
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… manifold (#3442) An open subset of a charted space is naturally a charted space. If the charted space has structure groupoid `G` (with `G` closed under restriction), then the open subset does also. Most of the work is in `topology/local_homeomorph`, where it is proved that a local homeomorphism whose source is `univ` is an open embedding, and conversely.
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An open subset of a charted space is naturally a charted space. If the charted space has structure groupoid
G(withGclosed under restriction), then the open subset does also.Most of the work is in
topology/local_homeomorph, where it is proved that a local homeomorphism whose source isunivis an open embedding, and conversely.I wrote this as an exercise in the
local_homeomorphlemmas. Feel free to close this PR if it doesn't fit well in the library (for example, if it should follow later from more general theory).