Theorems · Theorem · general topology
disjoint_nhds_nhdsSet
∀ {X : Type u_1} [inst : TopologicalSpace X] [RegularSpace X] {x : X} {s : Set X},
Disjoint (nhds x) (nhdsSet s) ↔ x ∉ closure s- Defined in
- Mathlib.Topology.Separation.Regular
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceRegularSpace
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Filterstatement · cited by 8,121
- nhdsstatement · cited by 5,554
- Disjointstatement · cited by 2,201
- closurestatement · cited by 1,254
- nhdsSetstatement · cited by 267
- RegularSpacestatement and proof · cited by 63
- disjoint_commproof · cited by 49
- disjoint_nhdsSet_nhdsproof · cited by 2
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