International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/3960 2020 2020 Department of Mathematics, Al-Balqa Applied University, Alsalt, Jordan Amani Amani Department of Mathematics, Faculty of Sciences, Al al-Bayt University, Mafraq, Jordan Ahmad Al Al-Omari In this paper, we will use the family of regular open sets in a topological space (Z, τ ) to define an operator ΦR : 2Z → 2Z by ΦR(F) = {s ∈ Z : ∃ D ∈ RO(Z, s) with (D − F )c ∈ P} in frame of primal topological spaces. Then we introduce the notion of topology δ-compatible for a primal in a primal topological space and study some of its properties. Finally, we use the concept of δ-semi-open sets to provide additional properties for the operators (⋄ R) and ΦR(F ), and we add many illustrative examples that help clarify the relationships between the concepts that are presented. 2026 2026 59 72 10.54216/IJNS.270106 https://www.americaspg.com/articleinfo/21/show/3960