Convergent nets in abelian topological groups

Robert Ledet

International Journal of Mathematics and Mathematical Sciences, 2001, vol. 27, 1-7

Abstract:

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 ℝ n in which any particular axis may be dense and Hausdorff group topologies on the torus in which S 1 is dense.

Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:186087

DOI: 10.1155/S016117120100744X

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