Some Categories of Compactness and Connectedness in Generalized Topological Spaces - Muhammad Shahbaz; Tayyab Kamran; Umar Ishtiaq; Mariam Imtiaz; Ioan-Lucian Popa; Fethi Mohamed Maiz (Axioms)
The presented work enhances the study of topological characteristics in non-classical circumstances by examining <semantics><msubsup>Sg*</msubsup></semantics>-compact and <semantics><msubsup>Sg*</msubsup></semantics>-connected spaces in the context of generalized topological spaces. The notions of <semantics><msubsup>Sg*</msubsup></semantics>-compactness and <semantics><msubsup>Sg*</msubsup></semantics>-connectedness are explored better to understand their characteristics and behavior in these generalized topologies. Further, the study implements the same extended contexts to investigate the separation axioms, particularly <semantics>T0</semantics>, <semantics>T1</semantics>, and <semantics>T2</semantics>. The structural consequences of these axioms, which are essential for categorizing topological spaces according to the distinctness of points and sets, are examined. Since the premises of <semantics><msubsup>Sg*</msubsup></semantics>-compactness and <semantics><msubsup>Sg*</msubsup></semantics>-connectedness are not directly related to the separation axioms, exploring them independently enhances the analysis of generalized topology. This study serves as theoretical insights and establishes the foundation for future research in generalized topological spaces, contributing to their continued evolution.