Theorems · Theorem · general topology

TendstoUniformlyOn.prodMk

∀ {α : Type u_1} {β : Type u_2} {ι : Type u_4} [inst : UniformSpace β] {F : ι → α → β} {f : α → β} {s : Set α}
  {p : Filter ι} {ι' : Type u_5} {β' : Type u_6} [inst_1 : UniformSpace β'] {F' : ι' → α → β'} {f' : α → β'}
  {p' : Filter ι'},
  TendstoUniformlyOn F f p s →
    TendstoUniformlyOn F' f' p' s →
      TendstoUniformlyOn (fun i a => (F i.1 a, F' i.2 a)) (fun a => (f a, f' a)) (p ×ˢ p') s

Defined in

Mathlib.Topology.UniformSpace.UniformConvergence

Cited by

4 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

UniformSpaceUniformSpace