Theorems · Theorem · sequences and series

Multipliable.tprod_mul_tprod_compl

∀ {α : Type u_1} {β : Type u_2} [inst : CommMonoid α] [inst_1 : TopologicalSpace α] {f : β → α} [T2Space α]
  [ContinuousMul α] {s : Set β},
  Multipliable (f ∘ Subtype.val) →
    Multipliable (f ∘ Subtype.val) → (∏' (x : ↑s), f ↑x) * ∏' (x : ↑sᶜ), f ↑x = ∏' (x : β), f x

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Basic

Cited by

0 results in Mathlib

Foundations

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

Assumes

CommMonoidTopologicalSpaceT2SpaceContinuousMul