International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 3, Pages 145-148
doi:10.1155/S0161171200003264
TΩ-sequences in abelian groups
Department of Mathematics, University of Louisiana at Lafayette, Lafayette 70504 1010, LA, USA
Received 19 April 1999
Copyright © 2000 Robert Ledet and Bradd Clark. 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 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.