TΩ-sequences in abelian groups

Abstract

A sequence in an abelian group is called aT-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 aTΩ-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 aTΩ-sequence and examples ofTΩ-sequences are given.