axiom countability of via semi open sets

Abstract

The paper intends to present a s-open sets and discuss some of its properties. and its relationship to open sets. also, they are used to introduce a specific form of countable space axioms called s-countable axioms, these include; S- separable spaces, s-first countability and s-second countability. Through the classical concept of topology, the properties of these spaces have been studied; moreover, we study the enumerated s-compounds and their behavior in some special spaces.