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Theorems · Theorem · general topology

Topology.isHomeomorph_iff_isStrictMap_bijective

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y},
  IsHomeomorph f ↔ Topology.IsStrictMap f ∧ Function.Bijective f

Homeomorphisms are precisely bijective strict maps.

Defined in
Mathlib.Topology.Maps.Strict.Basic
Cited by
1 results in Mathlib
Foundations
Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpace
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Around this declaration

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AddMonoidHom.isStrictMap_iff_isHomeomorph_quotientKerEquivRange · cited by 0AddMonoidHom.isStrictMap_…TopologicalSpace · cited by 24529TopologicalSpaceFunction.Bijective · cited by 863Function.BijectiveIsHomeomorph · cited by 69IsHomeomorphTopology.IsStrictMap · cited by 45Topology.IsStrictMapTopology.isHomeomorph_iff_isS…CITED BYCITES

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Cited by1

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