$\star$-$A_{\mathcal{I}}^\star$-sets and Decompositions of $\star$-$A_{\mathcal{I}}^\star$-continuity - O. Ravi; G. Selvi; S. Murugesan; S. Vijaya (International Journal of Mathematics And its Applications, 2015)
The aim of this paper is to introduce and study the notions of $\star$-$A_{\mathcal{I}}^\star$-sets and $\star$-C$_{\mathcal{I}}$-sets in ideal topological spaces. Properties of $\star$-$A_{\mathcal{I}}^\star$-sets and $\star$-C$_{\mathcal{I}}$-sets are investigated. Moreover, decompositions of $\star$-$A_{\mathcal{I}}^\star$-continuous functions via $\star$-$A_{\mathcal{I}}^\star$-sets and $\star$-C$_{\mathcal{I}}$-sets in ideal topological spaces are established.