Non metrizable topologies on Z with countable dual group
Algebraic Topology
2016-03-15 v1 General Topology
Group Theory
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 -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.
Cite
@article{arxiv.1603.03893,
title = {Non metrizable topologies on Z with countable dual group},
author = {Daniel de la Barrera Mayoral},
journal= {arXiv preprint arXiv:1603.03893},
year = {2016}
}