On the Topology τ_R^\diamond of Primal Topological Spaces

2024/02/13 by Murad Özkoç, Özkoç, Murad, Büşra KÖSTEL +1
Decision Sciences · #Fuzzy and Soft Set Theory

paper · pdf · doi:10.48550/arxiv.2402.08572

Abstract

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

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