Theorems · Theorem · sequences and series

Multipliable.map_tprod

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : CommMonoid α] [inst_1 : TopologicalSpace α] {f : β → α}
  {L : SummationFilter β} [L.NeBot] [inst_3 : CommMonoid γ] [inst_4 : TopologicalSpace γ] [T2Space γ],
  Multipliable f L →
    ∀ {G : Type u_4} [inst_6 : FunLike G α γ] [MonoidHomClass G α γ] (g : G),
      Continuous ⇑g → g (∏'[L] (i : β), f i) = ∏'[L] (i : β), g (f i)

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Basic

Cited by

3 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoidTopologicalSpaceSummationFilter.NeBotCommMonoidTopologicalSpaceT2SpaceFunLikeMonoidHomClass