Abstract:A space $X$ is {\it strongly star-Menger\/} if for each sequence $(\Cal U_n:n\in \Bbb N)$ of open covers of $X$, there exists a sequence $(K_n:n\in N)$ of finite subsets of $X$ such that $\{St(K_n,\Cal U_n):n\in \Bbb N\}$ is an open cover of $X$. In this paper, we investigate the relationship between strongly star-Menger spaces and related spaces, and also study topological properties of strongly star-Menger spaces.
Keywords: selection principles, strongly starcompact, strongly star-Menger, Alexandroff duplicate
AMS Subject Classification: 54D20 54C10