Sets Related to Openness and Continuity Decompositions in Primal Topological Spaces
DOI:
https://doi.org/10.29020/nybg.ejpam.v17i2.5171Keywords:
primal topological spaces,, P-open set,, P_R-sets,, Ψ_P -sets,, P-continuousAbstract
This paper introduces and investigates several new classes of sets called P-α-open sets, Psemiopen sets, P-preopen sets, and P-β-open sets within the framework of primal topological spaces. Their properties and relationships with other open set generalizations are studied through examples. Additionally, the concepts of PR-sets and PRα -sets are defined and their characteristics examined. Also, the notions of P-α-continuous, P-semicontinuous, P-precontinuous and P-β-continuous mappings are initiated and their features and main characterizations determined. A new class of sets called Ψ_P -sets is also introduced in primal topological spaces using the ΨP -operator. Their properties and relationships between Ψ_ P -sets, α-open, semi-open, and pre-open are investigated. Theorems on arbitrary unions and finite intersections of Ψ_P are discussed.
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