Groups whose same-order types are arithmetic progressions

Abstract

In this paper we continue our research about links and link topologies on ℓ-groups and Riesz spaces. We show that in a Riesz space E, a link topology   is a vector topology, if and only if the link consists of all order units in E. We also compare the link topologies with the positive lter topologies on an  ℓ-group. In addition, we provide some examples of these constructions.