Browsing by Author "Abushaheen, F.A."

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    Topologically indistinguishable relations and separation axioms
    (2024.01.01) Demiralp, S.; Al-shami, T.M.; Abushaheen, F.A.; El-latif, A.M.A.
    This study focuses on defining separation axioms for sets without an inherent topological structure. By utilizing a mapping to relate such sets to a topological space, we first define a distinguishable relation over the universal set with respect to the neighborhood systems inspired by a topology of the co-domain set and elucidate its basic properties. To facilitate the way of discovering this distinguishable relation, we initiate a color technique for the equivalence classes inspired by a given topology. Also, we provide an algorithm to determine distinguishable members (or objects) under study. Then, we establish a framework for introducing separation properties within these structureless sets and examine their master characterizations. To better understand the obtained results and relationships, we display some illustrative instances.