Abstract: We introduce the concept of γ-(α, β)-open sets and the concepts of γ-(α, β)-T_i spaces(i = 0, 1, 2, 3, 4) based on the concept of

(α, β)-open sets. We obtain some properties of γ-(α, β)-Tispaces. Furthermore, we study their essential characterization in topological space. 

Key words: γ-open sets, (α, β)-open sets, γ-(α, β)-open sets, γ-(α, β)-Tispaces