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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| Format: | Article |
| Language: | English |
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Wiley
2000-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171200003264 |
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| _version_ | 1849413201575280640 |
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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. |
| format | Article |
| id | doaj-art-74f719adb21841cdaaca077e848c09cc |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2000-01-01 |
| publisher | Wiley |
| record_format | Article |
| 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 |