Theorems · Theorem · general topology

tendsto_prod_top_iff

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

Uniform convergence to a constant function is equivalent to convergence in p ×ˢ ⊤.

Defined in

Mathlib.Topology.UniformSpace.UniformConvergence

Cited by

0 results in Mathlib

Foundations

Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

UniformSpace