Theorems · Theorem · general topology

TendstoLocallyUniformlyOn.prodMk

∀ {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} {s : Set α} {p : Filter ι} [inst_2 : UniformSpace γ] {G : ι → α → γ} {g : α → γ},
  TendstoLocallyUniformlyOn F f p s →
    TendstoLocallyUniformlyOn G g p s → TendstoLocallyUniformlyOn (fun n x => (F n x, G n x)) (fun x => (f x, g x)) p s

Defined in

Mathlib.Topology.UniformSpace.LocallyUniformConvergence

Cited by

7 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceUniformSpaceUniformSpace