Decompositions of continuity, ?-continuity and AB-continuity

The aim of this paper is to introduce the classes of alpha AB-sets, AC-sets and BC-sets which are weaker forms of AB-sets, AS-sets, S-sets and AC-sets, respectively. The relationships of between alpha AB-sets and the related sets and between AC-sets and BC-sets are discussed. By using alpha AB-sets, AC-sets, BC-sets and the related sets, new decompositions of alpha AB-continuity, alpha-continuity, continuity and AB-continuity are provided. (C) 2008 Elsevier Ltd. All rights reserved.