Theorems · Theorem · general topology
cauchy_iff_exists_le_nhds
∀ {α : Type u} [uniformSpace : UniformSpace α] [CompleteSpace α] {l : Filter α} [l.NeBot], Cauchy l ↔ ∃ x, l ≤ nhds x- Defined in
- Mathlib.Topology.UniformSpace.Cauchy
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- nhdsstatement and proof · 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
- Cauchystatement and proof · cited by 115
- CompleteSpace.completeproof · cited by 19
- cauchy_nhdsproof · cited by 7
- Cauchy.monoproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- cauchy_map_iff_exists_tendstoproof · cited by 4
- SeparatingDual.completeSpace_of_completeSpace_continuousLinearMapproof · cited by 1
- SeparatingDual.completeSpace_of_completeSpace_continuousMultilinearMapproof · cited by 1