Connectedness, local connectedness, and components on bipolar soft generalized topological spaces

Connectedness represents the most significant and fundamental topological property. It highlights main characteristics of spaces distinguishes one topology from another. There is a constant study bipolar soft generalized (\( \mathcal{BSGTS}s \)) by presenting \(\mathcal{BS}\) \( \widetilde{\widetilde{\mathfrak{g}}} \)-connected set space in \(\mathcal{BSGTS}s\) as well it discussing some properties results for these topics. Additionally, notion disjoint sets put forward, \(\mathcal{BS} \) \(\widetilde{\widetilde{\mathfrak{g}}}\)-separation set, \(\widetilde{\widetilde{\mathfrak{g}}}\)-separated \(\mathcal{BSS}s\) \)-hereditary Moreover, there an extensive \)-locally connected \)-component with related theorems following them, such concepts \mathcal{BS} \(\widetilde{\widetilde{\mathfrak{g}}}\)-locally \(\widetilde{\widetilde{\mathfrak{g}}}\)-connected are independent each other; also determined conditions under which subsets \(\widetilde{\widetilde{\mathfrak{g}}}\)-components.