In this paper, the notion of an operator γ on a supra topological space(X, μ) is studied and then utilized to analyze supra γ-open sets. The notions of μγ-g. closed sets on the subspace are introduced and investigated. Furthermore, some new μγ-separation axioms are formulated and the relationships between them are shown. Moreover, some characterizations of the new functions via operator γ on μ are presented and investigated. Finally, we give some properties of S(γ, β)-closed graph and strongly S(γ, β)-closed graph.