Final solution of Protasov-Comfort's problem on minimally almost periodic group topologies
Abstract
We prove that an abelian group admits a minimally almost periodic (MinAP) group topology if and only if it is connected in its Markov-Zariski topology. In particular, every unbounded abelian group admits a MinAP group topology. This answers positively a question set by Comfort, as well as several weaker forms proposed recently by Gabriyelyan. Using this characterization we answer also two open questions of Gould. We prove that a subgroup H of an abelian group G can be realized as the von Neumann kernel of G equipped with some Hausdorff group topology if and only if H is contained in the connected component of zero of G with respect to its Markov-Zariski topology. This completely resolves a question of Gabriyelyan, as well as some of its particular versions which were open.
Keywords
Cite
@article{arxiv.1410.3313,
title = {Final solution of Protasov-Comfort's problem on minimally almost periodic group topologies},
author = {Dikran Dikranjan and Dmitri Shakhmatov},
journal= {arXiv preprint arXiv:1410.3313},
year = {2014}
}