On $\beta^{*}-\mathrm{I}$-open Sets and $e^{*}-\mathrm{I}$-open Sets in Ideal Topological Spaces

In this study, we explore and delineate several characteristics of $\beta^{*}-\mathrm{I}$ -open sets, and $e^{*}-\mathrm{I}$ -open sets within ideal topological spaces. Additionally, we establish connections between $e^{*}$ -I-open sets, and $\beta^{*}$ -I-open sets in these spaces. Ultimately, we achieve a decomposition of continuity, enhancing the understanding of how these sets interact and contribute to the broader topological framework.