Free topological groups over metrizable spaces
type: Item
instance of: scholarly article
title: Free topological groups over metrizable spaces
zbMATH Open document ID: 0689.54009
DOI: 10.1016/0166-8641(89)90088-6
author: A. V. Arhangel'skii
author: Oleg Okunev
author: Vladimir G. Pestov
published in: Topology and its Applications
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://polipapers.upv.es/index.php/AGT/article/view/1961
review text: The structure of the free topological group F(X) over a metrizable space X as well as the structure of the Abelian free topological group A(X) over X are investigated. The main results obtained by the authors can be summarized as follows: (1) the tightness of F(X) is countable iff X is separable or discrete; (2) F(X) is a k-space iff X is locally compact or discrete; (3) the tightness of A(X) is countable iff the set \(X'\) (of all non-isolated points of X) is separable; (4) A(X) is a k-space iff X is locally compact and \(X'\) is separable. This yields the negative answer to a question raised by \textit{M. M. Choban} [Tr. Mosk. Mat. O.-va. 48, 106- 149 (1985; Zbl 0606.22003)].
Mathematics Subject Classification ID: 54C40
Mathematics Subject Classification ID: 54A25
Mathematics Subject Classification ID: 54D50
Mathematics Subject Classification ID: 22A99
zbMATH DE Number: 4129596
zbMATH Keywords: \(\aleph _ 0\)-spaces
zbMATH Keywords: free topological group
zbMATH Keywords: metrizable space
zbMATH Keywords: tightness
zbMATH Keywords: k-space
reviewed by: Aleksander Błaszczyk
MaRDI profile type: Publication
OpenAlex ID: W1979961643
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description: scientific article; zbMATH DE number 4129596