Generalized rough sets based on reflexive and transitive relations

In this paper. we investigate the relationship between generalized rough sets induced by reflexive and transitive relations and the topologies on the universe which is not restricted to be finite. It is proved that there exists a one-to-one correspondence between the set of all reflexive and transitive relations and the set of all topologies which satisfy a certain kind of compactness condition. (C) 2008 Elsevier Inc. All rights reserved.