Theorems · Theorem · general topology

TendstoUniformlyOnFilter.prodMap

∀ {α : Type u_1} {β : Type u_2} {ι : Type u_4} [inst : UniformSpace β] {F : ι → α → β} {f : α → β} {p : Filter ι}
  {p' : Filter α} {ι' : Type u_5} {α' : Type u_6} {β' : Type u_7} [inst_1 : UniformSpace β'] {F' : ι' → α' → β'}
  {f' : α' → β'} {q : Filter ι'} {q' : Filter α'},
  TendstoUniformlyOnFilter F f p p' →
    TendstoUniformlyOnFilter F' f' q q' →
      TendstoUniformlyOnFilter (fun i => Prod.map (F i.1) (F' i.2)) (Prod.map f f') (p ×ˢ q) (p' ×ˢ q')

Defined in

Mathlib.Topology.UniformSpace.UniformConvergence

Cited by

2 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

UniformSpaceUniformSpace