Demiralp, S.Al-shami, T.M.Abushaheen, F.A.El-latif, A.M.A.2024-05-212024-05-212024.01.01https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=dspace_ku&SrcAuth=WosAPI&KeyUT=WOS:001219715800001&DestLinkType=FullRecord&DestApp=WOS_CPLhttps://hdl.handle.net/20.500.12597/33167This 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.eninfo:eu-repo/semantics/openAccessfT-topological distinguishabilityequivalence relationseparation axiomsArticle10.3934/math.20247580012197158000011570115723962473-6988