Theorems · Theorem · general topology

UniformEquicontinuousOn.equicontinuousOn

∀ {ι : Type u_1} {α : Type u_6} {β : Type u_8} [uα : UniformSpace α] [uβ : UniformSpace β] {F : ι → β → α} {S : Set β},
  UniformEquicontinuousOn F S → EquicontinuousOn F S

Uniform equicontinuity on a subset implies equicontinuity on that subset.

Defined in

Mathlib.Topology.UniformSpace.Equicontinuity

Cited by

0 results in Mathlib

Foundations

Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

UniformSpaceUniformSpace