The semi-T3-separation axiom of Khalimsky topological spaces

The paper initially studies both the s-T3-separation and semi-T3-separation axiom of Khalimsky (K-for brevity) topological spaces. To do this work, first we investigate some properties semi-open semi-closed sets with respect to operations union or intersection further, a homeomorphism, semi-homeomorphism. Next, study various semi-topological K-topological spaces such as simple K-paths. Finally, after introducing notion which is broader than axiom, find sufficient necessary condition for space satisfy axiom.