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 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 U of X, there exists a countable subset (respectively, a Lindelöf subspace) F of X such that St(F, U)=X. In this paper, we give a characterization when the product _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 _i ≤ n A_i is star countable if and only if it is star Lindelöf.