Operators and separation axioms within the framework of diving topological spaces

Operators serve as fundamental tools in the analysis of topological spaces, prompting extensive research and yielding numerous significant results. In this paper, we introduced a new topological framework called the 'diving topological space', which was developed based on the diving structure. Within this framework, several operators were introduced, including one that fulfilled the Kuratowski axioms. We examined the core properties of these operators and explored the interrelations among them. Additionally, two new topologies were formulated and investigated with respect to each other and in comparison to classical topology. The study culminated by introducing concepts of fuzzy diving structures and demonstrating applications of fundamental topological properties, all substantiated with illustrative examples.