The Mackey topology problem: A complete solution for bounded groups

Abstract

We show that the Mackey topologies exist in the class LIN2 of linearly topologized Hausdorff groups and we give a complete description of these topologies in terms of B-embedded subgroups. As a consequence, we obtain also a complete description of the Mackey topologies in the class of locally quasi convex bounded abelian groups. This gives as a corollary the following result recently proved in [3]: every metrizable locally quasi convex bounded abelian group is Mackey. Further, we show that a locally quasi-convex group topology on a bounded abelian group is the Mackey topology if every countable subgroup H satisfies |H∧|<c.