On a New Operator Based on a Primal and its Associated Topology

This paper aims to introduce and study two new operators (.)^ω and cl^ω(·) by utilizing the notion of primal defined by S. Acharjee et al. Also, we investigate some fundamental properties of them. In addition, we showed that the operator cl^ω(.) satisfied the Kuratowski closure axioms. Therefore, we obtain a new topology denoted by τ^ω, which is finer than the original one. Moreover, the topology τ^ω obtained via the operator cl^ω(·) is finer than τω, where τω is the family of all ω-open subsets of a primal topological space (X,τ,P). Furthermore, we not only examine the fundamental properties of this class of sets but also provide some counterexamples.