Weakly strongly star-Menger spaces

A space \(X\) is called weakly strongly star-Menger space if for each sequence (\(\mathcal{U}_{n} : n \in \omega\)) of open covers of \(X\), there is a sequence \((F_n : n\in\omega)\) of finite subsets of \(X\) such that \(\overline{\bigcup_{n\in\omega} St(F_n, \mathcal{U}_n)}\) is \(X\). In this paper, we investigate the relationship of weakly strongly star-Menger spaces with other related spaces. It is shown that a Hausdorff paracompact weakly star Menger \(P\)-space is star-Menger. We also study the images and preimages of weakly strongly star-Menger spaces under various type of maps.