Absolutely strongly star-Menger spaces

A space X is absolutely strongly star-Menger if for each sequence (Un:n∈N) of open covers of X and each dense subset D of X, there exists a sequence (Fn:n∈N) of finite subsets of D such that {St(Fn,Un):n∈N} is an open cover of X. In this paper, we investigate the relationships between absolutely strongly star-Menger spaces and related spaces, and also study topological properties of absolutely strongly star-Menger spaces.