We first introduce 20 weak forms of continuity, which are closely related to 5 known weak forms of continuity. Then we classify them into 9 groups and give 12 decompositions of continuity. 1. Introduction. Continuity is one of the most important concepts in mathematics. In order to find deep properties of continuity, many weak forms of continuity were introduced in the literature. For instance, we have Levine's weak continuity [2] and semicontinuity [3], M. K. Singal and A. R. Singal's almost… CONTINUE READING