Theorems · Theorem · general topology

TendstoLocallyUniformlyOn.tendsto_at

∀ {α : Type u_1} {β : Type u_2} {ι : Type u_4} [inst : TopologicalSpace α] [inst_1 : UniformSpace β] {F : ι → α → β}
  {f : α → β} {s : Set α} {p : Filter ι},
  TendstoLocallyUniformlyOn F f p s → ∀ {a : α}, a ∈ s → Filter.Tendsto (fun i => F i a) p (nhds (f a))

Defined in

Mathlib.Topology.UniformSpace.LocallyUniformConvergence

Cited by

11 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceUniformSpace