A Lindelöf group with non-Lindelöf square
In the paper under review, the authors prove that there is a hereditarily Lindelöf group whose square is neither normal nor weakly paracompact. This answers in the negative an old question of Arhangelskiĭ whether normality, weak paracompactness, paracompactness, or the Lindelöf property of a~topological group is inherited by its square. The construction is inspired by the paper of \textit{J. T. Moore} [J. Am. Math. Soc. 19, No. 3, 717--736 (2006; Zbl 1107.03056)] and by an analysis of this paper by Repovš and Zdomskyy. The Todorcevic's technique of minimal walks is applied. A~byproduct of the presented solution to the Arhangelskiĭ question is a~strong negative partition relation on~\(\omega_1\) by constructing a~complex coloring mapping \(c:[\omega]^2\to\omega_1\).
scientific article; zbMATH DE number 6824539
scientific article