On the topology τ^R of primal topological spaces

The main purpose of this paper is to introduce and study two new operators (·)R^ and clR^(·) via primal, which is a new notion. We show that the operator clR^(·) is a Kuratowski closure operator, while the operator (·)R^ is not. In addition, we prove that the topology on X, shown as τR^, obtained by means of the operator clR^(·), is finer than τδ, where τδ is the family of δ-open subsets of a space (X, τ). Moreover, we not only obtain a base for the topology τR^ but also prove many fundamental results concerning this new structure. Furthermore, we provide many counterexamples related to our results.