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Theorems · Theorem · general topology

UniformContinuousOn.of_restrict

∀ {α : Type ua} {β : Type ub} [inst : UniformSpace α] [inst_1 : UniformSpace β] {f : α → β} {s : Set α},
  UniformContinuous (s.domRestrict f) → UniformContinuousOn f s

Alias of the reverse direction of uniformContinuousOn_iff_restrict.

Defined in
Mathlib.Topology.UniformSpace.Basic
Cited by
0 results in Mathlib
Foundations
Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
UniformSpaceUniformSpace
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Set · 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.of_restri…CITED BYCITES

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