A note on dynamic relational systems

It is known that weak and strong definabilities are defined for multiple-source approximation systems by Khan and Banerjee. This paper presents, in a more general setting a discussion on definabilities of sets in dynamic relational systems. We prove that the inverse-image of a weak or strong definable set with respect to relation preserving function is also weak or strong definable set, respectively. On the way, we show that the inverse-image of a reduct of attribute set is also a reduct under the object function of an information system homomorphism. Further, we give the connections between definable sets and the topology determined by the intersections of the topologies of reflexive relations. A quasi-uniformity is a filter on the cartesian product of a given universe satisfying certain conditions. In fact, every quasi-uniformity is a dynamic relational system where the relations are reflexive. In this respect, we discuss on the connections between approximation systems and (quasi) uniformities.