Non metrizable topologies on Z with countable dual group.

Daniel de la Barrera Mayoral

doi:10.4995/agt.2017.4469

Non metrizable topologies on Z with countable dual group.

Daniel de la Barrera Mayoral

DOI: https://doi.org/10.4995/agt.2017.4469

Abstract

In this paper we give two families of non-metrizable topologies on the group of the integers having a countable dual group which is isomorphic to a infinite torsion subgroup of the unit circle in the complex plane. Both families are related to D-sequences, which are sequences of natural numbers such that each term divides the following. The first family consists of locally quasi-convex group topologies. The second consists of complete topologies which are not locally quasi-convex. In order to study the dual groups for both families we need to make numerical considerations of independent interest.

Keywords

Locally quasi-convex topology; D-sequence; continuous character; infinite torsion subgroups of T.

Subject classification

2010 Mathematics Subject Classification

Primary: 22A05, 55M05. Secondary: 20K45.

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References

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