Theorems · Theorem · general topology
cauchySeq_iff_tendsto
∀ {α : Type u} {β : Type v} [uniformSpace : UniformSpace α] [Nonempty β] [inst : SemilatticeSup β] {u : β → α},
CauchySeq u ↔ Filter.Tendsto (Prod.map u u) Filter.atTop (uniformity α)- Defined in
- Mathlib.Topology.UniformSpace.Cauchy
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 69 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.
- Filter.Tendstostatement and proof · cited by 3,814
- Filter.atTopstatement and proof · cited by 2,405
- UniformSpacestatement and proof · cited by 2,040
- SemilatticeSupstatement and proof · cited by 785
- uniformitystatement and proof · cited by 765
- CauchySeqstatement · cited by 131
- Filter.prod_atTop_atTop_eqproof · cited by 20
- Prod.map_defproof · cited by 6
- cauchy_map_iff'proof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- Filter.HasBasis.cauchySeq_iffproof · cited by 5
- cauchySeq_of_controlledproof · cited by 2
- cauchySeq_iff'proof · cited by 0
- cauchySeq_iff_tendsto_dist_atTop_0proof · cited by 0
- CauchySeq.subseq_subseq_memproof · cited by 0