Note on “Generalized rough sets based on reflexive and transitive relations”

In this note, we show that, in the paper [Generalized rough sets based on reflexive and transitive relations, Information Sciences 178 (2008) 4138–4141], the topology induced by a preorder (i.e., a reflexive and transitive binary relation) is nothing but the well-known Alexandrov topology of the preorder. In addition, we point out that a topology satisfying certain kind of compactness condition proposed in the above mentioned paper is exactly an Alexandrov topology.