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Theorems · Theorem · general topology

IsClosed.isLindelof

∀ {X : Type u} [inst : TopologicalSpace X] {s : Set X} [LindelofSpace X], IsClosed s → IsLindelof s
Defined in
Mathlib.Topology.Compactness.Lindelof
Cited by
2 results in Mathlib
Foundations
Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceLindelofSpace
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Around this declaration

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

IsClosed.HasSeparatingCover · cited by 0IsClosed.HasSeparatingCov…Topology.IsClosedEmbedding.LindelofSpace · cited by 0IsClosedEmbedding.Lindelo…Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceIsClosed · cited by 1639IsClosedSet.subset_univ · cited by 228Set.subset_univIsLindelof · cited by 85IsLindelofLindelofSpace · cited by 24LindelofSpaceisLindelof_univ · cited by 6isLindelof_univIsLindelof.of_isClosed_subset · cited by 1IsLindelof.of_isClosed_su…IsClosed.isLindelofCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.