Theorems · Theorem · sequences and series

Function.Surjective.summable_iff_of_hasSum_iff

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : AddCommMonoid α] [inst_1 : TopologicalSpace α] {α' : Type u_4}
  [inst_2 : AddCommMonoid α'] [inst_3 : TopologicalSpace α'] {e : α' → α},
  Function.Surjective e →
    ∀ {f : β → α} {g : γ → α'}, (∀ {a : α'}, HasSum f (e a) ↔ HasSum g a) → (Summable f ↔ Summable g)

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Basic

Cited by

2 results in Mathlib

Foundations

Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidTopologicalSpaceAddCommMonoidTopologicalSpace