Volume 26 • Issue 1 • PP: 322-334 • 2025
The Topology T (PR⋆) ^⊛ in the Frame of Primal Topological Spaces
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© 2025 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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In this paper, we will use the family of regular⁺-open subsets to present and examine two new operators (.){PR⁺}⊛ and Cl{PR⁺}⊛. We demonstrate that, in contrast to the operator (.){PR⁺}⊛, the operator Cl{PR⁺}⊛ is a Kuratowski closure operator. We show that each of these operators lies between two previously defined operators where for each subset H⊆S, H_Pᶲ⊆H_{PR⁺}⊛⊆H_PRᶲ and H⊆Cl_Pᶲ(H)⊆Cl_{PR⁺}⊛(H)⊆Cl_{PR}ᶲ(H). Furthermore, we show that the topology, denoted by T_{PR⁺}⊛, which is obtained by Cl_{PR⁺}⊛ is independent from T and it is finer than T_η⁺, where T_η⁺ is the family of all unions of regular⁺-open subsets of (S, T). Then we demonstrate several fundamental results concerning this new structure and present many illustrative examples that relate to our conclusions. Finally, by using the operator Cl_{PR⁺}⊛ we introduce a new notion namely, P-generalized closed sets, and study some of their basic properties.
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