Theorems · Theorem · sequences and series

NonarchimedeanGroup.cauchySeq_prod_of_tendsto_cofinite_one

∀ {α : Type u_1} {G : Type u_2} [inst : CommGroup G] [inst_1 : UniformSpace G] [IsUniformGroup G]
  [NonarchimedeanGroup G] {f : α → G}, Filter.Tendsto f Filter.cofinite (nhds 1) → CauchySeq fun s => ∏ i ∈ s, f i

Let G be a nonarchimedean multiplicative abelian group, and let f : α → G be a function that tends to one on the filter of cofinite sets. For each finite subset of α, consider the partial product of f on that subset. These partial products form a Cauchy filter.

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Nonarchimedean

Cited by

1 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommGroupUniformSpaceIsUniformGroupNonarchimedeanGroup