Theorems · Theorem · sequences and series

MultipliableLocallyUniformlyOn.comp

∀ {α : Type u_1} {β : Type u_2} {ι : Type u_3} [inst : CommMonoid α] {f : ι → β → α} {s : Set β}
  [inst_1 : UniformSpace α] [inst_2 : TopologicalSpace β] {γ : Type u_4} [inst_3 : TopologicalSpace γ] {t : Set γ},
  MultipliableLocallyUniformlyOn f s →
    ∀ (h' : γ → β), Set.MapsTo h' t s → ContinuousOn h' t → MultipliableLocallyUniformlyOn (fun i y => f i (h' y)) 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

CommMonoidUniformSpaceTopologicalSpaceTopologicalSpace