Weakly strongly star-Menger spaces

Abstract

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.

Keywords

• stronlgy star-menger
• star-menger
• almost star-menger
• weakly star-menger
• covering topological spaces