In 1965, Njastad  introduced the notion of α-sets in topological space. In 1983, Mashhour et al.  introduced, with the help of α-sets, a weak form of continuity which they termed as α-continuity. Noiri  introduced the same concept, but under the name strong semicontinuity. Noiri  defined with the aid of α-sets a new weakened form of continuous mapping called weakly α-continuous mapping. Sen and Bhattacharyya  introduced another new weakened form of continuity called weak ∗α-continuity and proved that a mapping is α-continuous if and only if it is weakly α-continuous and weak ∗α-continuous. In this paper, we give a general setting for such decompositions of α-continuity by using expansion of α-open sets, whereas in , Tong used expansion of open sets to give a general setting for the decomposition of continuous mapping into weakly continuous and weak ∗ continuous mappings.
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