Minimally almost periodic group topology on infinite countable Abelian groups: A solution to Comfort's question

Abstract

For any countable subgroup $H$ of an unbounded Abelian group $G$ there is a complete Hausdorff group topology $\tau$ such that $H$ is the von Neumann radical of $(G,\tau )$. In particular, we obtain the positive answer to Comfort's question: any unbounded countable Abelian group admits a complete Hausdorff minimally almost periodic (MinAP) group topology. A bounded infinite Abelian group admits a MinAP group topology if and only if all its leading Ulm-Kaplansky invariants are infinite. If, in addition, $G$ is countably infinite, a MinAP group topology can be chosen to be complete.

References in corpus (3)

• The Markov-Zariski topology of an abelian group
• Almost maximally almost-periodic group topologies determined by T-sequences
• Which infinite abelian groups admit an almost maximally almost-periodic group topology?