Some Separation Axioms in the category Ord of Ordered sets: Application in Alexandroff Topology, Specifically on Primal Spaces

Maryam G. Alshehri, Sami Lazaar, Abdelwaheb Mhemdi, Neama Zidani


An order is any binary relation which is reflexive, transitive and anti-symmetric. Our main goal in this paper is to introduce some new binary relations between partial order and equality. Some implications between them and counterexamples ar clarified. Taking an Alexandroff $T_0$-space $(X,\tau)$, we study the order $\leq_{\tau}$. Finally, the particular caseĀ  $\leq_{f}$, where $f$ is a giving map from a set $X$ to itself, is explained.


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