Abstract
The aim of this paper is to introduce the classes of α AB -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 α AB -sets and the related sets and between AC -sets and BC -sets are discussed. By using α AB -sets, AC -sets, BC -sets and the related sets, new decompositions of α AB -continuity, α -continuity, continuity and AB -continuity are provided.
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