Non metrizable topologies on Z with countable dual group

Daniel de la Barrera Mayoral

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arXiv · 1603.03893

Non metrizable topologies on Z with countable dual group

Daniel de la Barrera Mayoral

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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.

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BibTeX RIS

Daniel de la Barrera Mayoral. 2016-03-12. Non metrizable topologies on Z with countable dual group. https://arxiv.org/abs/1603.03893

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