Theorems · Theorem · general topology

tendstoUniformlyOn_iff_seq_tendstoUniformlyOn

∀ {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}
  {l : Filter ι} [l.IsCountablyGenerated],
  TendstoUniformlyOn F f l s ↔
    ∀ (u : ℕ → ι), Filter.Tendsto u Filter.atTop l → TendstoUniformlyOn (fun n => F (u n)) f Filter.atTop s

Defined in

Mathlib.Topology.UniformSpace.UniformConvergence

Cited by

1 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

UniformSpaceFilter.IsCountablyGenerated