On partitions of groups into dense subsets
by
Yevhen Zelenyuk
Institute of Applied Problems of Mechanics & Mathematics, Lviv, Ukraine

In 1994 W.Comfort and J.van Mill proved that every nondiscrete Hausdorff topological Abelian group with finitely many elements of order 2 can be partitioned into two dense subsets. We prove that every infinite Abelian group with finitely many elements of order 2 can be partitioned into two subsets dense in any nondiscrete Hausdorff group topology.

Date received: May 19, 2001