In this paper, the mixed and ordinary operators are characterized in the classes of r-sets and r*-sets. Certain topological sets that are inherited from -open set [2], open set and -open set [13] are characterized using r -sets and r*-sets. More over the behavior of r-sets and r*-sets in spaces are investigated. The Inclusion chains among the mixed and ordinary operators are refined in the domains of r -sets and r*-sets.