Theorems · Theorem · general topology
uniformContinuousOn_iff_restrict
∀ {α : Type ua} {β : Type ub} [inst : UniformSpace α] [inst_1 : UniformSpace β] {f : α → β} {s : Set α},
UniformContinuousOn f s ↔ UniformContinuous (s.domRestrict f)- Defined in
- Mathlib.Topology.UniformSpace.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 74 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.
Cites11
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
- Filterproof · cited by 8,121
- Set.Elemstatement and proof · cited by 7,166
- Filter.Tendstoproof · cited by 3,814
- UniformSpacestatement and proof · cited by 2,040
- uniformityproof · cited by 765
- UniformContinuousstatement · cited by 410
- Set.domRestrictstatement and proof · cited by 383
- Filter.tendsto_map'_iffproof · cited by 50
- UniformContinuousOnstatement · cited by 47
- map_uniformity_set_coeproof · cited by 1
Cited by8
Results whose statement or proof uses this declaration.
- IsCompact.uniformContinuousOn_of_continuousproof · cited by 3
- UniformContinuousOn.continuousOnproof · cited by 3
- LipschitzOnWith.uniformContinuousOnproof · cited by 2
- UniformContinuousOn.restrictproof · cited by 1
- UniformContinuousOn.comp_tendstoUniformlyproof · cited by 1
- UniformContinuousOn.of_restrictproof · cited by 0
- Dynamics.coverEntropy_image_le_of_uniformContinuousOn_invariantproof · cited by 0
- Dynamics.coverEntropyInf_image_le_of_uniformContinuousOn_invariantproof · cited by 0