Star Lindelöfness of Products of Subspaces of Ordinals - Mou, Lei; Huang, Yanhui; Xu, Yanqin (Topology Proceedings, 2024)
For an infinite cardinal $κ$, a topological space $X$ is called $κ$-compact if every $F \subseteq X$ with $|F| ≥ κ$ has an accumulation point. A space $X$ is said to be star countable (respectively, star Lindelöf) if for every open cover $\mathcal{U}$ of $X$, there exists a countable subset (respectively, a Lindelöf subspace) $F$ of $X$ such that $\operatorname{St}(F, \mathcal{U})=X$. In this paper, we give a characterization when the product $\prod_{i ≤ n} A_i$ is $κ$-compact, where $κ>ω$ is regular, $n$ is a natural number, and each $A_i$ is a subspace of an ordinal $λ_i+1$. By using this result, we show that such a product $\prod_{i ≤ n} A_i$ is star countable if and only if it is star Lindelöf.