Theorems · Theorem · general topology
UniformContinuous.uniformContinuousOn
∀ {α : Type ua} {β : Type ub} [inst : UniformSpace α] [inst_1 : UniformSpace β] {f : α → β} {s : Set α},
UniformContinuous f → UniformContinuousOn f s- Defined in
- Mathlib.Topology.UniformSpace.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- UniformSpaceUniformSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- UniformSpacestatement and proof · cited by 2,040
- UniformContinuousstatement and proof · cited by 410
- UniformContinuousOnstatement · cited by 47
- Filter.tendsto_inf_leftproof · cited by 10
Cited by3
Results whose statement or proof uses this declaration.
- UniformContinuous.comp_tendstoLocallyUniformlyproof · cited by 6
- UniformContinuous.comp_tendstoLocallyUniformlyOnproof · cited by 6
- UniformContinuous.comp_uniformContinuousOnproof · cited by 0