The semi-T3-separation axiom of Khalimsky topological spaces

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