Theorems · Theorem · general topology
separatedNhds_iff_disjoint
∀ {X : Type u_1} [inst : TopologicalSpace X] {s t : Set X}, SeparatedNhds s t ↔ Disjoint (nhdsSet s) (nhdsSet t)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- IsOpenproof · cited by 2,400
- Disjointstatement and proof · cited by 2,201
- nhdsSetstatement · cited by 267
- SeparatedNhdsstatement · cited by 33
- hasBasis_nhdsSetproof · cited by 20
- Filter.HasBasis.disjoint_iffproof · cited by 13
Cited by2
Results whose statement or proof uses this declaration.
- completelyNormalSpace_iff_forall_isOpen_normalSpaceproof · cited by 3
- SeparatedNhds.disjoint_nhdsSetproof · cited by 2