Completeness of Lexicographic Products of GO-Spaces - Kemoto, Nobuyuki (Topology Proceedings, 2020)
Variations of Dedekind completeness of lexicographic products of GO-spaces are studied. As a corollary, we see that whenever $γ$ is limit and all GO-spaces $X_α$'s have minimal elements but have no maximal elements, connectedness of a lexicographic product $\prod_{α < γ} X_α$ implies non-connectedness of all $X_α$'s.