Topological space properties of rough sets

Abstract

The topological properties of the Pawlak rough sets model are discussed. The paper also points out that the map between the rough set model and the finite set can induce an equivalent relation on the finite set. If the map is regarded as a map between two topological spaces, then it is continuous. Furthermore, if the map is bijective, then it is simultaneously open and continuous, and the image and inverse image of the rough set are rough.