International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2000 / Article

Open Access

Volume 24 |Article ID 653516 | 4 pages | https://doi.org/10.1155/S0161171200003264

TΩ-sequences in abelian groups

Received19 Apr 1999

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 TΩ-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 TΩ-sequence and examples of TΩ-sequences are given.

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.


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