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Theorems · Theorem · general topology

Topology.IsOpenEmbedding.toOpenPartialHomeomorph_target

∀ {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).target = Set.range f
Defined in
Mathlib.Topology.OpenPartialHomeomorph.Basic
Cited by
5 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.

TopologicalSpace.Opens.openPartialHomeomorphSubtypeCoe_target · cited by 4Opens.openPartialHomeomor…Topology.IsOpenEmbedding.toOpenPartialHomeomorph_right_inv · cited by 2IsOpenEmbedding.toOpenPar…contMDiff_isOpenEmbedding · cited by 1contMDiff_isOpenEmbeddingcontMDiffOn_isOpenEmbedding_symm · cited by 1contMDiffOn_isOpenEmbeddi…EisensteinSeries.eisensteinSeries_tendstoLocallyUniformlyOn · cited by 1EisensteinSeries.eisenste…Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceSet.range · cited by 4705Set.rangePartialHomeomorph.toPartialEquiv · cited by 917PartialHomeomorph.toParti…OpenPartialHomeomorph.toPartialHomeomorph · cited by 851OpenPartialHomeomorph.toP…PartialEquiv.target · cited by 650PartialEquiv.targetSet.image_univ · cited by 322Set.image_univTopology.IsOpenEmbedding · cited by 231Topology.IsOpenEmbeddingTopology.IsOpenEmbedding.toOpenPartialHomeomorph · cited by 14IsOpenEmbedding.toOpenPar…IsOpenEmbedding.toOpenPartial…CITED BYCITES

Cites9

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Cited by5

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