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Theorems · Theorem · general topology

SeparatedNhds.disjoint_nhdsSet

∀ {X : Type u_1} [inst : TopologicalSpace X] {s t : Set X}, SeparatedNhds s t → Disjoint (nhdsSet s) (nhdsSet t)

Alias of the forward direction of separatedNhds_iff_disjoint.

Defined in
Mathlib.Topology.Separation.SeparatedNhds
Cited by
2 results in Mathlib
Foundations
Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

disjoint_nhdsSet_nhdsSet · cited by 0disjoint_nhdsSet_nhdsSetIsCompact.disjoint_nhdsSet_nhds · cited by 0IsCompact.disjoint_nhdsSe…Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceFilter · cited by 8121FilterDisjoint · cited by 2201DisjointnhdsSet · cited by 267nhdsSetSeparatedNhds · cited by 33SeparatedNhdsseparatedNhds_iff_disjoint · cited by 2separatedNhds_iff_disjointSeparatedNhds.disjoint_nhdsSetCITED BYCITES

Cites7

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Cited by2

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