Further Study of $\omega$-closed Sets

Abstract

In 1982, the notions of $\omega$-closed sets and $\omega$-open sets were introduced and studied by Hdeib [4]. In 2009, Noiri et al [6] introduced some generalizations of $\omega$-open sets and investigated some properties of the sets. Moreover, they used them to obtain decompositions of continuity. Quite Recently Ravi et al [7] studied further generalizations of $\omega$-open sets in topological spaces. In this paper we introduce new classes of functions in topological spaces and study the characterizations of such functions in detail. Finally we obtain some decomposition theorems.