A Lindelöf group with non-Lindelöf square
type: Item
instance of: scholarly article
title: A Lindelöf group with non-Lindelöf square
zbMATH Open document ID: 1382.22004
author: Yinhe Peng
author: Liuzhen Wu
published in: Advances in Mathematics
publication date: 2018-01-11T00:00:00Z
review text: 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 \(c:[\omega]^2\to\omega_1\).
reviewed by: Miroslav Repický
Mathematics Subject Classification ID: 22A10
Mathematics Subject Classification ID: 54D20
Mathematics Subject Classification ID: 03E02
Mathematics Subject Classification ID: 03E75
zbMATH DE Number: 6824539
zbMATH Keywords: minimal walk
zbMATH Keywords: Lindelöf topological group
zbMATH Keywords: strong negative partition relation
zbMATH Keywords: \(L\)~space
MaRDI profile type: Publication
full work available at URL: j.aim.2017.11.021
OpenAlex ID: W2774570060
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DOI: 10.1016/J.AIM.2017.11.021
description: scientific article; zbMATH DE number 6824539