Theorems · Theorem · general topology

TendstoUniformlyOn.comp

∀ {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}
  {s : Set α} {p : Filter ι},
  TendstoUniformlyOn F f p s → ∀ (g : γ → α), TendstoUniformlyOn (fun n => F n ∘ g) (f ∘ g) p (g ⁻¹' s)

Composing on the right by a function preserves uniform convergence on a set

Defined in

Mathlib.Topology.UniformSpace.UniformConvergence

Cited by

2 results in Mathlib

Foundations

Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

UniformSpace