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Theorems · Theorem · general topology

IsClosed.isCompletelyMetrizableSpace

∀ {X : Type u_1} [inst : TopologicalSpace X] [TopologicalSpace.IsCompletelyMetrizableSpace X] {s : Set X},
  IsClosed s → TopologicalSpace.IsCompletelyMetrizableSpace ↑s

A closed subset of a completely metrizable space is also completely metrizable.

Defined in
Mathlib.Topology.Metrizable.CompletelyMetrizable
Cited by
0 results in Mathlib
Foundations
Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpace.IsCompletelyMetrizableSpace
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Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceSet.Elem · cited by 7166Set.ElemIsClosed · cited by 1639IsClosedIsClosed.isClosedEmbedding_subtypeVal · cited by 19IsClosed.isClosedEmbeddin…TopologicalSpace.IsCompletelyMetrizableSpace · cited by 7TopologicalSpace.IsComple…Topology.IsClosedEmbedding.IsCompletelyMetrizableSpace · cited by 1IsClosedEmbedding.IsCompl…IsClosed.isCompletelyMetrizab…CITED BYCITES

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