Faintly m-continuous functions

We introduce a new class of functions called a faintly m-continuous function which is a generalization of both faintly continuous functions [Kyungpook Math. J. 22 (1982) 7] and m-continuous functions [Mem. Fac. Sci. Kochi Univ. Ser. A Math. 22 (2001) 9]. By this function, we try to unify several generalizations of faintly continuous functions.