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On decompositions of Irg-continuityKeywords: $mathcal{I}$-${rg}$-open sets , $mathcal{I}$-${galpha^{**}}$-open sets , $mathcal{I}$-${gpr}$- open sets , $mathcal{I}$-$C_r$-sets , $mathcal{I}$-${C_r}^{*}$-sets and $mathcal{I}$-${rg}$-continuity. Abstract: We introduce the notions of $mathcal{I}$-$rg$-open sets, $mathcal{I}$-$galpha^{**}$-open sets, $mathcal{I}$-$gpr$-open sets, $mathcal{I}$-$C_r$-sets and $mathcal{I}$-${C_r}^{*}$-sets to obtain the decompositions of $mathcal{I}$-$rg$-continuity in ideal topological spaces.
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