$\star$-$A_{\mathcal{I}}^\star$-sets and Decompositions of $\star$-$A_{\mathcal{I}}^\star$-continuity
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Keywords:
$\star$-$A_{\mathcal{I}}^\star$-set, $\star$-C$_{\mathcal{I}}$-set, C$_{\mathcal{I}}^\star$-set, pre-$\mathcal{I}$-regular set, ideal topological space, decompositionAbstract
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.
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