Theorems · Theorem · general topology

tendstoLocallyUniformlyOn_iff_tendstoUniformlyOn_of_compact

∀ {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}, IsCompact s → (TendstoLocallyUniformlyOn F f p s ↔ TendstoUniformlyOn F f p s)

For a compact set s, locally uniform convergence on s is just uniform convergence on s.

Defined in

Mathlib.Topology.UniformSpace.LocallyUniformConvergence

Cited by

5 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceUniformSpace