Theorems · Theorem · general topology
UniformContinuousOn.continuousOn
∀ {α : Type ua} {β : Type ub} [inst : UniformSpace α] [inst_1 : UniformSpace β] {f : α → β} {s : Set α},
UniformContinuousOn f s → ContinuousOn f s- Defined in
- Mathlib.Topology.UniformSpace.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 76 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.
Cites7
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
- ContinuousOnstatement · cited by 1,411
- UniformContinuous.continuousproof · cited by 66
- continuousOn_iff_continuous_domRestrictproof · cited by 51
- UniformContinuousOnstatement and proof · cited by 47
- uniformContinuousOn_iff_restrictproof · cited by 8
Cited by3
Results whose statement or proof uses this declaration.
- AbsolutelyContinuousOnInterval.continuousOnproof · cited by 2
- LipschitzOnWith.continuousOnproof · cited by 1
- HolderOnWith.continuousOnproof · cited by 0