Theorems · Theorem · sequences and series

Function.Surjective.tprod_eq_tprod_of_hasProd_iff_hasProd

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : CommMonoid α] [inst_1 : TopologicalSpace α] [T2Space α]
  {α' : Type u_4} [inst_3 : CommMonoid α'] [inst_4 : TopologicalSpace α'] {e : α' → α},
  Function.Surjective e →
    e 1 = 1 →
      ∀ {f : β → α} {g : γ → α'}, (∀ {a : α'}, HasProd f (e a) ↔ HasProd g a) → ∏' (b : β), f b = e (∏' (c : γ), g c)

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Basic

Cited by

1 results in Mathlib

Foundations

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

Assumes

CommMonoidTopologicalSpaceT2SpaceCommMonoidTopologicalSpace