Theorems · Theorem · general topology
Cauchy.le_nhds_lim
∀ {α : Type u} [uniformSpace : UniformSpace α] [CompleteSpace α] {f : Filter α} (hf : Cauchy f), f ≤ nhds f.lim- Defined in
- Mathlib.Topology.UniformSpace.Cauchy
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- UniformSpaceCompleteSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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 · cited by 5,554
- CompleteSpacestatement and proof · cited by 2,532
- UniformSpacestatement and proof · cited by 2,040
- SProd.sprodstatement · cited by 1,750
- Filter.NeBotstatement · cited by 853
- uniformitystatement · cited by 765
- Cauchystatement and proof · cited by 115
- CompleteSpace.completeproof · cited by 19
- Filter.limstatement · cited by 10
- le_nhds_limproof · cited by 5
- Filter.NeBot.nonemptystatement · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- CauchySeq.tendsto_limUnderproof · cited by 3
- CauchyFilter.inseparable_lim_iffproof · cited by 1