Counterpart of Boundary Topological Operators Within the Framework of Primal Topological Spaces

Murad Özkoç, Faical Yacine Issaka, A. A. Azzam and Tareq M. Al-shami

International Journal of Mathematics and Mathematical Sciences, 2026, vol. 2026, 1-11

Abstract: In this paper, we aim to introduce a new operator via primal topological spaces, called the ⊤-operator, and look into its basic properties. Among the interesting results we prove, for every subset D, we have (1) D⊤⊆FrD, where Fr is the topological boundary operator, and (2) D⊤=∅, whenever either a subset D or its complement lies outside the given primal, which significantly reduces the computational cost of algorithms designed to compute the ⊤-operator. We also demonstrate how the ⊤-operator interacts with some other operators, such as the operator ⋄ and the operator Ψ, in the literature. Although the operator ⊤ does not appear as a boundary operator, we obtain a basis by means of this operator, and so we get a topology, namely, ⊤-topology. By illustrative example, we establish the independence between ⊤-topology and ⋄-topology. Finally, we get a new pseudoclosure operator through the ⊤-operator and determine the relationship between the ⊤-operator and the closure operator when a subset is open or closed.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:2123865

DOI: 10.1155/ijmm/2123865

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