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.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2014
- DOI:
- 10.48550/arXiv.1410.3313
- arXiv:
- arXiv:1410.3313
- Bibcode:
- 2014arXiv1410.3313D
- Keywords:
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- Mathematics - General Topology;
- Mathematics - Group Theory