Theorems · Theorem · general topology

IsOpen.tendstoLocallyUniformlyOn_iff_forall_tendsto

∀ {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},
  IsOpen s →
    (TendstoLocallyUniformlyOn F f p s ↔
      ∀ x ∈ s, Filter.Tendsto (fun y => (f y.2, F y.1 y.2)) (p ×ˢ nhds x) (uniformity β))

Defined in

Mathlib.Topology.UniformSpace.LocallyUniformConvergence

Cited by

2 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceUniformSpace