Theorems · Theorem · general topology

tendstoLocallyUniformlyOn_TFAE

∀ {α : Type u_1} {β : Type u_2} {ι : Type u_4} [inst : TopologicalSpace α] [inst_1 : UniformSpace β] {s : Set α}
  [LocallyCompactSpace α] (G : ι → α → β) (g : α → β) (p : Filter ι),
  IsOpen s →
    [TendstoLocallyUniformlyOn G g p s, ∀ K ⊆ s, IsCompact K → TendstoUniformlyOn G g p K,
        ∀ x ∈ s, ∃ v ∈ nhdsWithin x s, TendstoUniformlyOn G g p v].TFAE

Defined in

Mathlib.Topology.UniformSpace.LocallyUniformConvergence

Cited by

1 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceUniformSpaceLocallyCompactSpace