Theorems · Theorem · general topology
CauchyFilter.uniformContinuous_extend
∀ {α : Type u} [inst : UniformSpace α] {β : Type v} [inst_1 : UniformSpace β] [CompleteSpace β] {f : α → β},
UniformContinuous (CauchyFilter.extend f)- Defined in
- Mathlib.Topology.UniformSpace.Completion
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CompleteSpacestatement and proof · cited by 2,532
- UniformSpacestatement and proof · cited by 2,040
- UniformContinuousstatement and proof · cited by 410
- Nonempty.someproof · cited by 340
- CauchyFilterstatement and proof · cited by 19
- uniformContinuous_uniformly_extendproof · cited by 6
- CauchyFilter.isUniformInducing_pureCauchyproof · cited by 6
- CauchyFilter.denseRange_pureCauchyproof · cited by 5
- uniformContinuous_of_constproof · cited by 4
- CauchyFilter.extendstatement · cited by 2
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