Theorems · Theorem · general topology

tendstoLocallyUniformlyOn_iff_forall_isCompact

∀ {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} [LocallyCompactSpace α],
  IsOpen s → (TendstoLocallyUniformlyOn F f p s ↔ ∀ K ⊆ s, IsCompact K → TendstoUniformlyOn F f p K)

Defined in

Mathlib.Topology.UniformSpace.LocallyUniformConvergence

Cited by

8 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceUniformSpaceLocallyCompactSpace