Theorems · Theorem · sequences and series

Multipliable.tprod_eq_one_iff

∀ {ι : Type u_1} {α : Type u_3} [inst : CommMonoid α] [inst_1 : PartialOrder α] [IsOrderedMonoid α]
  [CanonicallyOrderedMul α] [inst_4 : TopologicalSpace α] [OrderClosedTopology α] {f : ι → α},
  Multipliable f → (∏' (i : ι), f i = 1 ↔ ∀ (x : ι), f x = 1)

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Order

Cited by

1 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoidPartialOrderIsOrderedMonoidCanonicallyOrderedMulTopologicalSpaceOrderClosedTopology