Theorems · Theorem · general topology
Filter.TotallyBounded.exists_clusterPt
∀ {α : Type u} [uniformSpace : UniformSpace α] [CompleteSpace α] {f : Filter α} [f.NeBot],
f.TotallyBounded → ∃ x, ClusterPt x f- Defined in
- Mathlib.Topology.UniformSpace.Cauchy
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Filterstatement and proof · cited by 8,121
- nhdsproof · cited by 5,554
- CompleteSpacestatement and proof · cited by 2,532
- UniformSpacestatement and proof · cited by 2,040
- Filter.NeBotstatement and proof · cited by 853
- Ultrafilterproof · cited by 193
- Ultrafilter.toFilterproof · cited by 172
- ClusterPtstatement · cited by 138
- Cauchyproof · cited by 115
- ClusterPt.monoproof · cited by 30
- Filter.TotallyBoundedstatement and proof · cited by 24
- CompleteSpace.completeproof · cited by 19
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