Some Decompositions of Weaker Form of Continuity

Abstract

In this paper we introduce the notions of $\alpha$gs-$\mathcal{I}$-open sets, pgs-$\mathcal{I}$-open sets, sg-$\mathcal{I}$-open sets, $\omega$$_t$-$\mathcal{I}$-sets, $\omega$$_{\alpha^*}$-$\mathcal{I}$-sets and $\omega$$_S$-$\mathcal{I}$-sets in ideal topological spaces and investigate some of their properties. Using these notions we obtain decompositions of $\omega$-continuity.