International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 2, Pages 221-234
doi:10.1155/S0161171298000325
Quasiorders, principal topologies, and partially ordered partitions
Department of Mathematics, Western Kentucky University, Bowling Green 42101, Kentucky, USA
Received 26 August 1996; Revised 30 April 1997
Copyright © 1998 Thomas A. Richmond. 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 quasiorders on a set X are equivalent to the topologies on X which are closed
under arbitrary intersections. We consider the quaisorders on X to be partial orders on the blocks
of a partition of X and use this approach to survey some fundamental results on the lattice of
quasiorders on X.