Novel Categories of Spaces in the Frame of Generalized Fuzzy Topologies via Fuzzy gµ-Closed Sets

One of the known approaches to studying topological concepts is to utilize subclasses of topology, such as clopen sets and generalized closed sets. In this study, we apply the notion of fuzzy generalized µ-closed sets (Fgµ-closed sets) to establish and analyze novel categories of spaces, namely Fgµ-regular, Fgµ-normal, and Fµ-symmetric spaces in the frame of generalized fuzzy topology (GFT). We investigate the fundamental properties of these classes, exploring their unique characteristics and preservation theorems under Fgµ-continuous maps. We establish the interrelationships between these classes and the other separation axioms in this setting, and we demonstrate that Fµ-regular, Fµ-normal, and Fµ-symmetric spaces are special cases of Fgµ-regular, Fgµ-normal, and Fµ-T₁ spaces, respectively. Additionally, we show that the equivalence for these cases hold when the GFT is Fµ-T1 . The connections between these classes and 2 their counterparts in the crisp GT are studied. Finally, we discuss these classes’ hereditary and topological properties, further enhancing our comprehension of their behavior and implications.