Theorems · Theorem · sequences and series

cauchySeq_finset_iff_prod_vanishing

∀ {α : Type u_1} {β : Type u_2} [inst : UniformSpace α] [inst_1 : CommGroup α] [IsUniformGroup α] {f : β → α},
  (CauchySeq fun s => ∏ b ∈ s, f b) ↔ ∀ e ∈ nhds 1, ∃ s, ∀ (t : Finset β), Disjoint t s → ∏ b ∈ t, f b ∈ e

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Group

Cited by

3 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

UniformSpaceCommGroupIsUniformGroup