Theorems · Theorem · general topology
totallyBounded_iff_filter
∀ {α : Type u} [uniformSpace : UniformSpace α] {s : Set α},
TotallyBounded s ↔ ∀ (f : Filter α), f.NeBot → f ≤ Filter.principal s → ∃ c ≤ f, Cauchy c- Defined in
- Mathlib.Topology.UniformSpace.Cauchy
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- UniformSpace
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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
- Filterstatement and proof · cited by 8,121
- UniformSpacestatement and proof · cited by 2,040
- Filter.NeBotstatement and proof · cited by 853
- Filter.principalstatement and proof · cited by 740
- Cauchystatement and proof · cited by 115
- TotallyBoundedstatement · cited by 79
- Filter.totallyBounded_principal_iffproof · cited by 6
- Filter.totallyBounded_iff_filterproof · cited by 2
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