b∗-I-Open Sets and Their Role in Weaker Forms of Paracompactness

This paper introduces and investigates two new notions of paracompactness in ideal topological spaces: \(b^*\)-\(\mathcal{I}\)-paracompactness and \(b_1^*\)-\(\mathcal{I}\)-paracompactness. These concepts generalize classical paracompactness using \(b^*\)-\(\mathcal{I}\)-open sets and ideal-related refinements. We establish fundamental properties of these spaces, including their preservation under subspaces, finite unions, and continuous mappings. Furthermore, we provide characterizations of these spaces and compare them with existing variants such as \(\beta\)-paracompactness, \(\beta_1\)-paracompactness and \(\mathcal{I}\)-paracompactness, supported by illustrative examples. Our results extend the theory of ideal topological spaces and offer a framework for future studies on generalized covering properties.