Theorems · Theorem · general topology

UniformContinuous.comp_tendstoUniformlyOnFilter

∀ {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} {p' : Filter α} [inst_1 : UniformSpace γ] {g : β → γ},
  UniformContinuous g → TendstoUniformlyOnFilter F f p p' → TendstoUniformlyOnFilter (fun i => g ∘ F i) (g ∘ f) p p'

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

Defined in

Mathlib.Topology.UniformSpace.UniformConvergence

Cited by

7 results in Mathlib

Foundations

Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

UniformSpaceUniformSpace