A New Operator via Regular Open Sets in a New Topological Structure
Amani Rawshdeh1,∗, Ahmad Al-Omari2
1Department of Mathematics, Al-Balqa Applied University, Alsalt-Jordan
2Department of Mathematics, Faculty of Sciences, Al al-Bayt University, Mafraq, Jordan
Emails: amanirawshdeh@bau.edu.jo; omarimutah1@yahoo.com
Abstract
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.
Keywords: Primal; Primal topological spaces; The operator ΦR(F ); τ ⋄
R-topology; δ-compatible