@article{Demiralp2024, 
author = {S. Demiralp and Tareq M. Al-shami and Fuad A. Abushaheen and Alaa M. Abd El-latif},
title = {Topologically indistinguishable relations and separation axioms},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {6},
pages = {15701-15723},
keywords = {fT-topological distinguishability, equivalence relation, separation axioms},
url = {https://www.sciopen.com/article/10.3934/math.2024758},
doi = {10.3934/math.2024758},
abstract = {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.}
}