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Theorems · Theorem · general topology

IsLocalHomeomorph.isOpenEmbedding_of_injective

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y},
  IsLocalHomeomorph f → Function.Injective f → Topology.IsOpenEmbedding f

An injective local homeomorphism is an open embedding.

Defined in
Mathlib.Topology.IsLocalHomeomorph
Cited by
1 results in Mathlib
Foundations
Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpace
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Around this declaration

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IsLocalHomeomorph.isOpenEmbedding_of_comp · cited by 1IsLocalHomeomorph.isOpenE…TopologicalSpace · cited by 24529TopologicalSpaceTopology.IsOpenEmbedding · cited by 231Topology.IsOpenEmbeddingIsLocalHomeomorph · cited by 35IsLocalHomeomorphTopology.IsOpenEmbedding.of_continuous_injective_isOpenMap · cited by 13IsOpenEmbedding.of_contin…IsLocalHomeomorph.isOpenMap · cited by 4IsLocalHomeomorph.isOpenM…IsLocalHomeomorph.continuous · cited by 1IsLocalHomeomorph.continu…IsLocalHomeomorph.isOpenEmbed…CITED BYCITES

Cites6

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