Convergent nets in abelian topological groups

Robert Ledet
2001 International Journal of Mathematics and Mathematical Sciences  
A net in an abelian group is called aT-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 onℝnin which any particular axis may be
more » ... lar axis may be dense and Hausdorff group topologies on the torus in whichS1is dense.
doi:10.1155/s016117120100744x fatcat:ip7zlhrz3fe27l2hvclh3kpcrm