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International Journal of Mathematics and Mathematical Sciences - Volume 24 2000, Issue 3, Pages 145-148

Department of Mathematics, University of Louisiana at Lafayette, Lafayette 70504 1010, LA, USA

Received 19 April 1999

Copyright © 2000 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A sequence in an abelian group is called a T-sequence if thereexists a Hausdorff group topology in which the sequence convergesto zero. This paper describes the fundamental system for the finestgroup topology in which this sequence converges to zero. A sequenceis a TΩ-sequence if there exist uncountably many differentHausdorff group topologies in which the sequence converges to zero.The paper develops a condition which insures that a sequence is aTΩ-sequence and examples of TΩ-sequences are given.





Author: Robert Ledet and Bradd Clark

Source: https://www.hindawi.com/



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