International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 3, Pages 145-148
doi:10.1155/S0161171200003264

TΩ-sequences in abelian groups

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.