Theorems · Theorem · general topology

UniformContinuousOn.comp_tendstoLocallyUniformly

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {ι : Type u_4} [inst : TopologicalSpace α] [inst_1 : UniformSpace β]
  {F : ι → α → β} {f : α → β} {p : Filter ι} [inst_2 : UniformSpace γ] {g : β → γ} {t : Set β},
  UniformContinuousOn g t →
    TendstoLocallyUniformly F f p →
      (∀ (x : α), f x ∈ t) →
        (∀ᶠ (n : ι) in p, ∀ (x : α), F n x ∈ t) → TendstoLocallyUniformly (fun x => g ∘ F x) (g ∘ f) p

Defined in

Mathlib.Topology.UniformSpace.LocallyUniformConvergence

Cited by

1 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceUniformSpaceUniformSpace