Theorems · Theorem · general topology
Equiv.toEquiv_toHomeomorphOfContinuousClosed
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] (e : X ≃ Y)
(h₁ : Continuous ⇑e) (h₂ : IsClosedMap ⇑e), (e.toHomeomorphOfContinuousClosed h₁ h₂).toEquiv = e- Defined in
- Mathlib.Topology.Homeomorph.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- Equivstatement and proof · cited by 8,337
- Continuousstatement and proof · cited by 2,592
- IsClosedMapstatement and proof · cited by 138
- Homeomorph.toEquivstatement and proof · cited by 77
- Equiv.toHomeomorphOfContinuousClosedstatement and proof · cited by 4
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