Theorems · Theorem · general topology

Continuous.tendstoUniformly

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : UniformSpace α] [inst_1 : UniformSpace β]
  [WeaklyLocallyCompactSpace α] [CompactSpace β] [inst_4 : UniformSpace γ] (f : α → β → γ),
  Continuous ↿f → ∀ (x : α), TendstoUniformly f (f x) (nhds x)

A continuous family of functions α → β → γ tends uniformly to its value at x if α is weakly locally compact and β is compact.

Defined in

Mathlib.Topology.UniformSpace.HeineCantor

Cited by

0 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

UniformSpaceUniformSpaceWeaklyLocallyCompactSpaceCompactSpaceUniformSpace