Mathlib Map

Theorems · Theorem · general topology

UniformContinuousOn.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)

Alias of the forward direction of uniformContinuousOn_iff_restrict.

Defined in
Mathlib.Topology.UniformSpace.Basic
Cited by
1 results in Mathlib
Foundations
Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
UniformSpaceUniformSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cauchy.map_of_le · cited by 0Cauchy.map_of_leSet · cited by 53352SetSet.Elem · cited by 7166Set.ElemUniformSpace · cited by 2040UniformSpaceUniformContinuous · cited by 410UniformContinuousSet.domRestrict · cited by 383Set.domRestrictUniformContinuousOn · cited by 47UniformContinuousOnuniformContinuousOn_iff_restrict · cited by 8uniformContinuousOn_iff_r…UniformContinuousOn.restrictCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.