A Decomposition of Continuity

Tong [11] introduced the notions of A-sets and A-continuity in topological spaces and established a decomposition of continuity. In [12], he also introduced the notions of B-sets and B-continuity and used them to obtain a new decomposition of continuity. Recently, Ganster and Reilly [3] have improved Tong's decomposition result and provided a decomposition of A-continuity. Quite recently, Przemski [10] has obtained some decompositions of continuity and weak continuity. In this paper, we introduce the notions of a*-sets and C-continuity and obtain another decomposition of continuity.