T Ω -sequences in abelian groups

Robert Ledet and Bradd Clark

International Journal of Mathematics and Mathematical Sciences, 2000, vol. 24, 1-4

Abstract:

A sequence in an abelian group is called a T -sequence if there exists a Hausdorff group topology in which the sequence converges to zero. This paper describes the fundamental system for the finest group topology in which this sequence converges to zero. A sequence is a T Ω -sequence if there exist uncountably many different Hausdorff group topologies in which the sequence converges to zero. The paper develops a condition which insures that a sequence is a T Ω -sequence and examples of T Ω -sequences are given.

Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:653516

DOI: 10.1155/S0161171200003264

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