Theorems · Theorem · general topology
IsCompact.nhds_hausdorff_eq_nhds_vietoris
∀ {α : Type u_1} [inst : UniformSpace α] {s : Set α}, IsCompact s → nhds s = nhds sA compact set has the same neighborhoods in the Hausdorff uniformity and the Vietoris topology.
- Defined in
- Mathlib.Topology.UniformSpace.Closeds
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- UniformSpace
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Cites34
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
- Filterstatement · cited by 8,121
- Set.ofPredproof · cited by 6,101
- Set.imageproof · cited by 5,609
- nhdsstatement and proof · cited by 5,554
- LE.le.transproof · cited by 3,151
- Set.Nonemptyproof · cited by 2,627
- Set.iUnionproof · cited by 2,483
- IsOpenproof · cited by 2,400
- le_antisymmproof · cited by 2,068
- UniformSpacestatement and proof · cited by 2,040
- Filter.univ_mem'proof · cited by 1,672
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