Theorems · Theorem · general topology

tendsto_prod_filter_iff

∀ {α : Type u_1} {β : Type u_2} {ι : Type u_4} [inst : UniformSpace β] {F : ι → α → β} {p : Filter ι} {p' : Filter α}
  {c : β}, Filter.Tendsto (↿F) (p ×ˢ p') (nhds c) ↔ TendstoUniformlyOnFilter F (fun x => c) p p'

Uniform convergence on a filter p' to a constant function is equivalent to convergence in p ×ˢ p'.

Defined in

Mathlib.Topology.UniformSpace.UniformConvergence

Cited by

2 results in Mathlib

Foundations

Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

UniformSpace