The paper aims to introduce a novel class of separation axioms on topological ordered spaces, namely Tci -ordered spaces (i = 0, 1 , 1, 1 1 , 2). They are defined by utilizing the notion of limit points of a set. With the aid of some examples, we scrutinize the 22 relationships between them as well as their relationships with strong Ti-ordered and Ti-spaces. Also, we investigate the interrelations between some of the initiated ordered separation axioms and some topological notions such as continuous topological ordered spaces and disconnected spaces. Furthermore, we verify that these ordered separation axioms are preserved under ordered embedding homeomorphism mappings and give a sufficient condition to be hereditary properties. Eventually, we demonstrate that the product of Tci -ordered spaces is also Tci -ordered for each i ̸= 2.
Digital Object Identifier (DOI)
M. Al-shami, Tareq and Abo-Elhamayel, M.
"Novel Class of Ordered Separation Axioms using Limit Points,"
Applied Mathematics & Information Sciences: Vol. 14:
6, Article 17.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol14/iss6/17