Theorems · Theorem · sequences and series

NonarchimedeanGroup.multipliable_iff_tendsto_cofinite_one

∀ {α : Type u_1} {G : Type u_2} [inst : CommGroup G] [inst_1 : UniformSpace G] [IsUniformGroup G]
  [NonarchimedeanGroup G] [CompleteSpace G] (f : α → G), Multipliable f ↔ Filter.Tendsto f Filter.cofinite (nhds 1)

Let G be a complete nonarchimedean multiplicative abelian group. Then a function f : α → G is unconditionally multipliable if and only if it tends to one on the filter of cofinite sets.

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Nonarchimedean

Cited by

0 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommGroupUniformSpaceIsUniformGroupNonarchimedeanGroupCompleteSpace