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: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2000-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171200003264 |
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| Summary: | 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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| ISSN: | 0161-1712 1687-0425 |