r-Near topologies on nearness approximation spaces

Abstract

In this manuscript, it is aimed to convert the topology on a set X which is on a nearness approximation space to new set families via indiscernibility relation. Then, if the open sets of the present topology are defined as the set of related elements, the set families, which have weakly related elements, will be obtained. Finally, the topological properties and concepts that these new families hold will be examined.