Theorems · Theorem · general topology
CauchySeq.totallyBounded_range
∀ {α : Type u} [uniformSpace : UniformSpace α] {s : ℕ → α}, CauchySeq s → TotallyBounded (Set.range s)Every Cauchy sequence over ℕ is totally bounded.
- Defined in
- Mathlib.Topology.UniformSpace.Cauchy
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 80 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.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Set.ofPredproof · cited by 6,101
- Set.imageproof · cited by 5,609
- Set.rangestatement · cited by 4,705
- le_reflproof · cited by 2,061
- UniformSpacestatement and proof · cited by 2,040
- le_rflproof · cited by 1,558
- uniformityproof · cited by 765
- le_totalproof · cited by 294
- CauchySeqstatement and proof · cited by 131
- Set.range_subset_iffproof · cited by 99
- Set.Finite.imageproof · cited by 96
Cited by1
Results whose statement or proof uses this declaration.
- Filter.Tendsto.isVonNBounded_rangeproof · cited by 1