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Theorems · Theorem · general topology

IsHomeomorph.isStrictMap

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

A homeomorphism is a strict map.

Defined in
Mathlib.Topology.Maps.Strict.Basic
Cited by
2 results in Mathlib
Foundations
Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Topology.IsStrictMap.id · cited by 2IsStrictMap.idTopology.IsHomeomorph.isStrictMap · cited by 0IsHomeomorph.isStrictMapTopologicalSpace · cited by 24529TopologicalSpaceIsHomeomorph · cited by 69IsHomeomorphTopology.IsStrictMap · cited by 45Topology.IsStrictMapIsHomeomorph.continuous · cited by 8IsHomeomorph.continuousIsHomeomorph.isOpenMap · cited by 6IsHomeomorph.isOpenMapIsOpenMap.isStrictMap · cited by 2IsOpenMap.isStrictMapIsHomeomorph.isStrictMapCITED BYCITES

Cites6

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Cited by2

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