On spaces with star kernel Menger

Given a topological property $$\mathcal{P}$$ , space $$X$$ is called star- if for any open cover $$\mathcal{U}$$ of the there exists set $$Y\subseteq X$$ with such that $$St(Y,\mathcal{U})=X$$ ; $$Y$$ star kernel . In this paper, we introduce and study spaces Menger, is, determined by Menger spaces, denoted $$S_{\rm fin}(\mathcal{O},\mathcal{O})$$ Some examples are given to show relationship some other related properties studied previously, behaviour respect subspaces, products, continuous images preimages investigated. Additionally, comments on selection principles theory given. Particularly, questions posed Song within addressed. Finally, several new introduced as well general them posed.