International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 11, Pages 645-651
doi:10.1155/S016117120100744X
Convergent nets in abelian topological groups
200 Wingfield Drive, Houma, LA 70360, USA
Received 30 April 2001
Copyright © 2001 Robert Ledet. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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 ℝn in which any
particular axis may be dense and Hausdorff group topologies on
the torus in which S1 is dense.