Theorems · Theorem · sequences and series

HasProdLocallyUniformlyOn.exists_hasProdUniformlyOn

∀ {α : Type u_1} {β : Type u_2} {ι : Type u_3} [inst : CommMonoid α] {f : ι → β → α} {g : β → α} {x : β} {s : Set β}
  [inst_1 : UniformSpace α] [inst_2 : TopologicalSpace β] [LocallyCompactSpace β],
  HasProdLocallyUniformlyOn f g s → s ∈ nhds x → ∃ t ∈ nhdsWithin x s, HasProdUniformlyOn f g t

Defined in

Mathlib.Topology.Algebra.InfiniteSum.UniformOn

Cited by

1 results in Mathlib

Foundations

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

Assumes

CommMonoidUniformSpaceTopologicalSpaceLocallyCompactSpace