Theorems · Theorem · general topology
CauchyFilter.extend_pureCauchy
∀ {α : Type u} [inst : UniformSpace α] {β : Type v} [inst_1 : UniformSpace β] [T0Space β] {f : α → β},
UniformContinuous f → ∀ (a : α), CauchyFilter.extend f (CauchyFilter.pureCauchy a) = f a- Defined in
- Mathlib.Topology.UniformSpace.Completion
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- UniformSpacestatement and proof · cited by 2,040
- UniformContinuousstatement and proof · cited by 410
- T0Spacestatement and proof · cited by 179
- CauchyFilterproof · cited by 19
- CauchyFilter.pureCauchystatement and proof · cited by 9
- CauchyFilter.isUniformInducing_pureCauchyproof · cited by 6
- CauchyFilter.denseRange_pureCauchyproof · cited by 5
- CauchyFilter.extendstatement · cited by 2
- uniformly_extend_of_indproof · cited by 1
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