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Theorems · Theorem · general topology

Topology.IsOpenEmbedding.toOpenPartialHomeomorph_source

∀ {X : Type u_1} {Y : Type u_3} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] (f : X → Y)
  (h : Topology.IsOpenEmbedding f) [inst_2 : Nonempty X],
  (Topology.IsOpenEmbedding.toOpenPartialHomeomorph f h).source = Set.univ
Defined in
Mathlib.Topology.OpenPartialHomeomorph.Basic
Cited by
3 results in Mathlib
Foundations
Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpaceNonempty
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Around this declaration

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

Topology.IsOpenEmbedding.singletonChartedSpace · cited by 6IsOpenEmbedding.singleton…Topology.IsOpenEmbedding.isManifold_singleton · cited by 2IsOpenEmbedding.isManifol…contMDiff_isOpenEmbedding · cited by 1contMDiff_isOpenEmbeddingTopology.IsOpenEmbedding.singleton_hasGroupoid · cited by 0IsOpenEmbedding.singleton…Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceSet.univ · cited by 3945Set.univPartialEquiv.source · cited by 964PartialEquiv.sourcePartialHomeomorph.toPartialEquiv · cited by 917PartialHomeomorph.toParti…OpenPartialHomeomorph.toPartialHomeomorph · cited by 851OpenPartialHomeomorph.toP…Topology.IsOpenEmbedding · cited by 231Topology.IsOpenEmbeddingTopology.IsOpenEmbedding.toOpenPartialHomeomorph · cited by 14IsOpenEmbedding.toOpenPar…IsOpenEmbedding.toOpenPartial…CITED BYCITES

Cites8

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Cited by4

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