Some new types of decomposition of continuity II

In this paper we extended (or generalized) the notions studied in [Carpintero, C. Moreno, J. and Rosas, E., Some New type of decomposition of continuity, submitted]. Using the notion of -regular open set and -semi regular open set, we introduce the concept of locally -regular semi closed sets and locally -semi regular semi closed sets and give a new theory of decomposition of continuity and some weak forms of continuity are studied. Also we improve some recent results due by [Roy, B. and Sen, R., On decomposition of weak continuity, Creat. Math. Inform, 24 (2015), No. 1-2, 83–88].