Theorems · Theorem · general topology

CompactSpace.uniformEquicontinuous_of_equicontinuous

∀ {α : Type u_1} {β : Type u_2} [inst : UniformSpace α] [inst_1 : UniformSpace β] {ι : Type u_4} {F : ι → β → α}
  [CompactSpace β], Equicontinuous F → UniformEquicontinuous F

An equicontinuous family of functions defined on a compact uniform space is automatically uniformly equicontinuous.

Defined in

Mathlib.Topology.UniformSpace.HeineCantor

Cited by

0 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

UniformSpaceUniformSpaceCompactSpace