Absolutely strongly star-Menger spaces

A space X is absolutely strongly star-Menger if for each sequence ( U n : n ∈ N ) of open covers of X and each dense subset D of X, there exists a sequence ( F n : n ∈ N ) of finite subsets of D such that { St ( F n , U n ) : 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.