Theorems · Theorem · general topology
Cauchy.map_of_le
∀ {α : Type u} {β : Type v} [uniformSpace : UniformSpace α] [inst : UniformSpace β] {f : Filter α} {m : α → β},
Cauchy f → ∀ {s : Set α}, UniformContinuousOn m s → f ≤ Filter.principal s → Cauchy (Filter.map m f)- Defined in
- Mathlib.Topology.UniformSpace.Cauchy
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- UniformSpaceUniformSpace
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Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Filterstatement and proof · cited by 8,121
- UniformSpacestatement and proof · cited by 2,040
- Filter.mapstatement and proof · cited by 819
- uniformityproof · cited by 765
- Filter.principalstatement and proof · cited by 740
- Filter.comapproof · cited by 546
- Cauchystatement and proof · cited by 115
- UniformContinuousOnstatement and proof · cited by 47
- inf_eq_leftproof · cited by 41
- Cauchy.mapproof · cited by 9
- Cauchy.comap'proof · cited by 3
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