Theorems · Theorem · general topology

UniformContinuous.comp_tendstoUniformly

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {ι : Type u_4} [inst : UniformSpace β] {F : ι → α → β} {f : α → β}
  {p : Filter ι} [inst_1 : UniformSpace γ] {g : β → γ},
  UniformContinuous g → TendstoUniformly F f p → TendstoUniformly (fun i => g ∘ F i) (g ∘ f) p

Composing on the left by a uniformly continuous function preserves uniform convergence

Defined in

Mathlib.Topology.UniformSpace.UniformConvergence

Cited by

9 results in Mathlib

Foundations

Depth 15 from the axioms · uses propext, Quot.sound

Assumes

UniformSpaceUniformSpace