Convergent nets in abelian topological groups

A net in an abelian group is called a T-net if there exists a Hausdorff group topology in which the net converges to 0. This paper describes a fundamental system for the finest group topology in which the net converges to 0. The paper uses this description to develop conditions which insure there ex...

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Bibliographic Details
Published in:International journal of mathematics and mathematical sciences 2001-01, Vol.27 (11), p.645-651
Main Author: Ledet, Robert
Format: Article
Language:English
Online Access:Get full text
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Summary:A net in an abelian group is called a T-net if there exists a Hausdorff group topology in which the net converges to 0. This paper describes a fundamental system for the finest group topology in which the net converges to 0. The paper uses this description to develop conditions which insure there exists a Hausdorff group topology in which a particular subgroup is dense in a group. Examples given include showing that there are Hausdorff group topologies on n in which any particular axis may be dense and Hausdorff group topologies on the torus in which S1 is dense.
ISSN:0161-1712
1687-0425
DOI:10.1155/S016117120100744