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

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.