Theorems · Theorem · sequences and series

hasProdLocallyUniformlyOn_of_forall_compact

∀ {α : Type u_1} {β : Type u_2} {ι : Type u_3} [inst : CommMonoid α] {f : ι → β → α} {g : β → α} {s : Set β}
  [inst_1 : UniformSpace α] [inst_2 : TopologicalSpace β],
  IsOpen s →
    ∀ [LocallyCompactSpace β], (∀ K ⊆ s, IsCompact K → HasProdUniformlyOn f g K) → HasProdLocallyUniformlyOn f g s

Defined in

Mathlib.Topology.Algebra.InfiniteSum.UniformOn

Cited by

3 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoidUniformSpaceTopologicalSpaceLocallyCompactSpace