On a New Operator Based on a Primal and its Associated Topology (European Journal of Pure and Applied Mathematics, 2024)
This paper aims to introduce and study two new operators $(.)^{\diamond}_{ω}$ and $cl^{\diamond}_{ω}(·)$ 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 $cl^{\diamond}_{ω}(.)$ satisfied the Kuratowski closure axioms. Therefore, we obtain a new topology denoted by $τ^{\diamond}_{ω},$ which is finer than the original one. Moreover, the topology $τ^{\diamond}_{ω}$ obtained via the operator $cl^{\diamond}_{ω}(·)$ is finer than $τ_{ω}$, where $τ_{ω}$ is the family of all $ω$-open subsets of a primal topological space $(X,τ,\mathcal{P}).$ Furthermore, we not only examine the fundamental properties of this class of sets but also provide some counterexamples.