International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 2, Pages 357-360
doi:10.1155/S0161171294000499
The meet of locally connected group topologies
Louisiana State University at Alexandria, 8100 Hwy 71 South, Alexandria 71302, LA, USA
Received 6 November 1992; Revised 23 March 1993
Copyright © 1994 Dorene J. Fox. 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
The collection of all group topologies on a given group is a complete lattice partially ordered by inclusion. The purpose of this paper is to develop a convenient method of defining the meet of an arbitrary collection of group topologies and demonstrate that the meet of a collection of locally connected group topologies is also locally connected.