Theorems · Theorem · general topology
OpenPartialHomeomorph.ofSet_trans_ofSet
∀ {X : Type u_1} [inst : TopologicalSpace X] {s : Set X} (hs : IsOpen s) {s' : Set X} (hs' : IsOpen s'),
(OpenPartialHomeomorph.ofSet s hs).trans (OpenPartialHomeomorph.ofSet s' hs') = OpenPartialHomeomorph.ofSet (s ∩ s') ⋯- Cited by
- 0 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
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Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.preimageproof · cited by 4,946
- IsOpenstatement and proof · cited by 2,400
- Set.extproof · cited by 2,266
- PartialEquiv.sourceproof · cited by 964
- PartialHomeomorph.toPartialEquivproof · cited by 917
- OpenPartialHomeomorph.toPartialHomeomorphproof · cited by 851
- OpenPartialHomeomorph.toFun'proof · cited by 745
- OpenPartialHomeomorphstatement and proof · cited by 664
- OpenPartialHomeomorph.symmproof · cited by 460
- IsOpen.interstatement and proof · cited by 98
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