Non metrizable topologies on Z with countable dual group.
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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.<br /><br />
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1996 ◽
Vol 144
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pp. 179-182
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2006 ◽
Vol 93
(3)
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pp. 545-569
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1969 ◽
Vol 35
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pp. 151-157
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2010 ◽
Vol 06
(07)
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pp. 1589-1607
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2001 ◽
Vol 04
(04)
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pp. 569-577
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2013 ◽
Vol 35
(4)
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pp. 1045-1055
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