Using the topology Tγ in a topological space (X,T ) , a new class of generalized open sets called Γ-preopen sets, is introduced and studied. This class generates a new topology T1 which is larger than Tα and smaller than Tγα . By means of the corresponding interior and closure operators, among other results, necessary and sufficient conditions are given for T1 to coincide with Tα , Tγ or Tγα .