Theorems · Theorem · Lie groups

hasSum_iff_hasSum_compl

∀ {α : Type u_1} {β : Type u_2} [inst : AddCommGroup α] [inst_1 : UniformSpace α] [inst_2 : IsUniformAddGroup α]
  {L : SummationFilter β} (f : β → α) (a : α), HasSum (⇑UniformSpace.Completion.toCompl ∘ f) (↑a) L ↔ HasSum f a L

A function f has a sum in a uniform additive group α if and only if it has that sum in the completion of α.

Defined in

Mathlib.Topology.Algebra.InfiniteSum.GroupCompletion

Cited by

1 results in Mathlib

Foundations

Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupUniformSpaceIsUniformAddGroup