Series with Commuting Terms in Topologized Semigroups

Abstract

We show that the following general version of the Riemann–Dirichlet theorem is true: if every rearrangement of a series with pairwise commuting terms in a Hausdorff topologized semigroup converges, then its sum range is a singleton.

Keywords

• semigroup
• group
• topology
• permutation
• convergence