Topological structure on generalized approximation space related to n-arry relation

Classical structure of rough set theory was first formulated by Z. Pawlak in [6]. The foundation of its object classification is an equivalence binary relation and equivalence classes. The upper and lower approximation operations are two core notions in rough set theory. They can also be seenas a closure operator and an interior operator of the topology induced by an equivalence relation on a universe. There are many studies on the relations between generalized rough set approximation and rough topological space. In this paper, We are defined some properties of an n-ary relation such as reflexive, symmetry, strongly symmetry, quasi-transitive, n- transitive and n-equivalence on a set . We introduce topological method to generalized rough set and study the relationship between topological theory and rough set theory. By using an n-ary tolerance relation and quasi-transitive relation, we define a topology on nonempty set . In the end, we prove some topological properties such as quasi-discreteness, connectivity, compactness, quasi-metric able, separateness.