TΩ-sequences in abelian groups

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 unc...

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Main Authors: Robert Ledet, Bradd Clark
Format: Article
Language:English
Published: Wiley 2000-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Subjects:
Online Access:http://dx.doi.org/10.1155/S0161171200003264
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author Robert Ledet
Bradd Clark
author_facet Robert Ledet
Bradd Clark
author_sort Robert Ledet
collection DOAJ
description 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.
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institution Kabale University
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publishDate 2000-01-01
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series International Journal of Mathematics and Mathematical Sciences
spelling doaj-art-74f719adb21841cdaaca077e848c09cc2025-08-20T03:34:12ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252000-01-0124314514810.1155/S0161171200003264TΩ-sequences in abelian groupsRobert Ledet0Bradd Clark1Department of Mathematics, University of Louisiana at Lafayette, Lafayette 70504 1010, LA, USADepartment of Mathematics, University of Louisiana at Lafayette, Lafayette 70504 1010, LA, USAA 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.http://dx.doi.org/10.1155/S0161171200003264Abelian topological groupHausdorffsequential convergence.
spellingShingle Robert Ledet
Bradd Clark
TΩ-sequences in abelian groups
International Journal of Mathematics and Mathematical Sciences
Abelian topological group
Hausdorff
sequential convergence.
title TΩ-sequences in abelian groups
title_full TΩ-sequences in abelian groups
title_fullStr TΩ-sequences in abelian groups
title_full_unstemmed TΩ-sequences in abelian groups
title_short TΩ-sequences in abelian groups
title_sort tω sequences in abelian groups
topic Abelian topological group
Hausdorff
sequential convergence.
url http://dx.doi.org/10.1155/S0161171200003264
work_keys_str_mv AT robertledet tōsequencesinabeliangroups
AT braddclark tōsequencesinabeliangroups