Decompositions of continuity, a-continuity and AB-continuity

The aim of this paper is to introduce the classes of aAB-sets, AC-sets and BC-sets which are weaker forms of AB-sets, AB-sets, B-sets and AC-sets, respectively. The relationships of between aAB-sets and the related sets and between AC-sets and BC-sets are discussed. By using aAB-sets, AC-sets, BC-sets and the related sets, new decompositions of aAB-continuity, a-continuity, continuity and AB-continuity are provided.