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Theorems · Theorem · general topology

closed_nhdsSet_basis

∀ {X : Type u_1} [inst : TopologicalSpace X] [NormalSpace X] (u : Set X),
  IsClosed u → (nhdsSet u).HasBasis (fun s => s ∈ nhdsSet u ∧ IsClosed s) id
Defined in
Mathlib.Topology.Separation.Regular
Cited by
1 results in Mathlib
Foundations
Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceNormalSpace
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Around this declaration

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

lift'_nhdsSet_closure · cited by 1lift'_nhdsSet_closureSet · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceFilter · cited by 8121FilterIsClosed · cited by 1639IsClosedFilter.HasBasis · cited by 604Filter.HasBasisnhdsSet · cited by 267nhdsSetNormalSpace · cited by 84NormalSpaceFilter.hasBasis_self · cited by 17Filter.hasBasis_selfexists_mem_nhdsSet_isClosed_subset · cited by 1exists_mem_nhdsSet_isClos…closed_nhdsSet_basisCITED BYCITES

Cites9

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Cited by1

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