An Exploration of Compactness and Separation Axioms in Generalized Primal Topological Spaces (European Journal of Pure and Applied Mathematics, 2025)
The research explores S∗g-compactness together with S∗g-connectedness in generalized primal topological spaces to enhance theoretical knowledge of non-classical topological systems. This paper provides an extensive analysis of these two concepts to show their characteristics and potential applications. The research examines the relationship dynamics between T0, T1, and T2 separation axioms and these concepts throughout their expanded theoretical framework. Examining S∗g-compactness and S∗g-connectedness independently provides an advanced understanding of generalized primal spaces, although they diverge from standard separation properties. This study simultaneously supports theoretical research of these domains while building essential foundations for math investigations in this field.
Keywords: generalized topological space; Hausdorff space; compactness; primal spaces.