Theorems · Theorem · general topology
Cauchy.ultrafilter_of
∀ {α : Type u} [uniformSpace : UniformSpace α] {l : Filter α} (h : Cauchy l), Cauchy ↑(Ultrafilter.of l)- Defined in
- Mathlib.Topology.UniformSpace.Cauchy
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 76 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.
Cites11
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
- LE.le.transproof · cited by 3,151
- UniformSpacestatement and proof · cited by 2,040
- SProd.sprodstatement · cited by 1,750
- Filter.NeBotstatement and proof · cited by 853
- uniformitystatement · cited by 765
- Ultrafilter.toFilterstatement and proof · cited by 172
- Cauchystatement and proof · cited by 115
- Ultrafilter.ofstatement and proof · cited by 15
- Ultrafilter.of_leproof · cited by 15
- Filter.prod_monoproof · cited by 14
Cited by1
Results whose statement or proof uses this declaration.
- isComplete_iff_ultrafilterproof · cited by 1