Theorems · Theorem · sequences and series

NonarchimedeanGroup.multipliable_of_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}, Filter.Tendsto f Filter.cofinite (nhds 1) → Multipliable f

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

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Nonarchimedean

Cited by

1 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommGroupUniformSpaceIsUniformGroupNonarchimedeanGroupCompleteSpace