Expansion of α-open sets and decomposition of α-continuous mappings

Abstract

In 1965, Njastad [2] introduced the notion of α-sets in topological space. In 1983, Mashhour et al. [1] introduced, with the help of α-sets, a weak form of continuity which they termed as α-continuity. Noiri [3] introduced the same concept, but under the name strong semicontinuity. Noiri [4] defined with the aid of α-sets a new weakened form of continuous mapping called weakly α-continuous mapping. Sen and Bhattacharyya [5] 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 [6], 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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