Theorems · Theorem · general topology
Filter.totallyBounded_iff_filter
∀ {α : Type u} [uniformSpace : UniformSpace α] {g : Filter α},
g.TotallyBounded ↔ ∀ (f : Filter α), f.NeBot → f ≤ g → ∃ c ≤ f, Cauchy c- Defined in
- Mathlib.Topology.UniformSpace.Cauchy
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- UniformSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites44
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- LE.le.transproof · cited by 3,151
- Compl.complproof · cited by 2,925
- le_reflproof · cited by 2,061
- UniformSpacestatement and proof · cited by 2,040
- Set.Finiteproof · cited by 1,814
- SProd.sprodproof · cited by 1,750
- iInfproof · cited by 1,690
Cited by2
Results whose statement or proof uses this declaration.
- Filter.totallyBounded_iff_ultrafilterproof · cited by 1
- totallyBounded_iff_filterproof · cited by 0