Theorems · Theorem · general topology
SeparatedNhds.of_singleton_finset
∀ {X : Type u_1} [inst : TopologicalSpace X] [T2Space X] {x : X} {s : Finset X}, x ∉ s → SeparatedNhds {x} ↑s- Defined in
- Mathlib.Topology.Separation.Hausdorff
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceT2Space
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- T2Spacestatement and proof · cited by 1,351
- Finset.coe_singletonproof · cited by 145
- SeparatedNhdsstatement and proof · cited by 33
- Finset.disjoint_singleton_leftproof · cited by 17
- SeparatedNhds.of_finset_finsetproof · cited by 2
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