A UNIFIED THEORY OF WEAKLY OPEN FUNCTIONS

Abstract. We introduce a new notion of weakly M-open functions as functions dened between sets satisfying some minimal conditions. We obtain some characterizations and several properties of such functions. The functions enable us to formulate a unied theory of weak openness [36], weak semi-openness [10], weak preopenness [11], and weak -openness [9]. 1. Introduction. In 1984, Rose [36] dened the notion of weakly open functions. Some properties of weakly open functions were studied in [5]. Semi-open sets, preopen sets, and -open sets play an important role in researching generalizations of open functions in topological spaces. By using these sets, Caldas and Navalagi [7{11] introduced and studied variou