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Theorems · Theorem · general topology

Topology.IsClosedEmbedding.locallyCompactSpace

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] [LocallyCompactSpace Y]
  {f : X → Y}, Topology.IsClosedEmbedding f → LocallyCompactSpace X
Defined in
Mathlib.Topology.Compactness.LocallyCompact
Cited by
3 results in Mathlib
Foundations
Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpaceLocallyCompactSpace
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Around this declaration

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

ProperSpace.of_locallyCompact_module · cited by 1ProperSpace.of_locallyCom…AbsoluteValue.Completion.locallyCompactSpace · cited by 0Completion.locallyCompact…Homeomorph.locallyCompactSpace_iff · cited by 0Homeomorph.locallyCompact…TopologicalSpace · cited by 24529TopologicalSpaceLocallyCompactSpace · cited by 324LocallyCompactSpaceTopology.IsClosedEmbedding · cited by 195Topology.IsClosedEmbeddingTopology.IsClosedEmbedding.isClosed_range · cited by 41IsClosedEmbedding.isClose…IsClosed.isLocallyClosed · cited by 12IsClosed.isLocallyClosedTopology.IsClosedEmbedding.isInducing · cited by 10IsClosedEmbedding.isInduc…Topology.IsInducing.locallyCompactSpace · cited by 4IsInducing.locallyCompact…IsClosedEmbedding.locallyComp…CITED BYCITES

Cites7

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Cited by3

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