Decompositions of continuity, αα-continuity and ABAB-continuity

The aim of this paper is to introduce the classes of αABαAB-sets, ACAC-sets and BCBC-sets which are weaker forms of ABAB-sets, ABAB-sets, BB-sets and ACAC-sets, respectively. The relationships of between αABαAB-sets and the related sets and between ACAC-sets and BCBC-sets are discussed. By using αABαAB-sets, ACAC-sets, BCBC-sets and the related sets, new decompositions of αABαAB-continuity, αα-continuity, continuity and ABAB-continuity are provided.