A separable normal topological group which is not Lindelöf
type: Item
instance of: scholarly article
title: A separable normal topological group which is not Lindelöf
zbMATH Open document ID: 0577.22005
DOI: 10.1016/0166-8641(85)90095-1
author: K. P. Hart
author: Jan van Mill
published in: Topology and its Applications
publication date: 1985-01-01T00:00:00Z
review text: An example mentioned in the title had been constructed under CH by \textit{A. Hajnal} and \textit{I. Juhász} [Gen. Topology Appl. 6, 199-205 (1976; Zbl 0323.22001)]; it was even hereditarily separable and hereditarily (collectionwise) normal. Now there is an example in ZFC, but without the hereditary properties. The construction is achieved by associating with each topological space X a semitopological group B(X) such that (a) X is a closed subspace of B(X), (b) the density is not increased, (c) B(X) is normal if all finite powers of X are normal, and (d) B(X) is a topological group if X is in addition sequentially compact (e.g.). Finally the authors show that the separable, normal, sequentially compact, non-compact space X of \textit{S. P. Franklin} and \textit{M. Rajagopalan} [Trans. Am. Math. Soc. 90, 305-314 (1971; Zbl 0217.481)] satisfies the condition in (c), and consequently B(X) is the desired example.
Mathematics Subject Classification ID: 22A05
Mathematics Subject Classification ID: 54A25
Mathematics Subject Classification ID: 54D20
Mathematics Subject Classification ID: 54D15
zbMATH DE Number: 3922998
zbMATH Keywords: non-Lindelöf topological group
zbMATH Keywords: CH
zbMATH Keywords: ZFC
zbMATH Keywords: separable
zbMATH Keywords: normal
reviewed by: Volker Eberhardt
MaRDI profile type: Publication
full work available at URL: 0166-8641(85)90095-1
OpenAlex ID: W2139013430
cites work: Q4150804
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description: scientific article; zbMATH DE number 3922998