Note on function spaces with the topology of pointwise convergence
type: Item
instance of: scholarly article
title: Note on function spaces with the topology of pointwise convergence
zbMATH Open document ID: 1035.54011
author: Jan van Mill
author: Jan Pelant
author: R. Pol
published in: Archiv der Mathematik
publication date: 2003-11-17T00:00:00Z
review text: The paper contains two examples of function spaces \(C_p(X)\) of continuous real-valued functions together with the topology of pointwise convergence. The first example is the Cook continuum. The author proves that for any Cook continuum \(M\) the space \(C_p(M)^n\) is uniformly homeomorphic to \(C_p(M)^m\) if and only if \(n=m\). The second example provides a negative answer to Problem 45 of [\textit{A. V. Arkhangel'skij}, Hvsek, M. (ed.) et al., Recent progress in general topology, Amsterdam: North Holland, 1--56 (1992; Zbl 0814.54009)].
Mathematics Subject Classification ID: 54C35
Mathematics Subject Classification ID: 54A20
Mathematics Subject Classification ID: 54G20
zbMATH DE Number: 2004965
zbMATH Keywords: function space
zbMATH Keywords: pointwise convergence
zbMATH Keywords: Cook continuum
zbMATH Keywords: Lindelöf space
reviewed by: Aleksandr A. Ivanov
MaRDI profile type: Publication
full work available at URL: s00013-003-0032-9
OpenAlex ID: W2136207802
DOI: 10.1007/S00013-003-0032-9
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description: scientific article; zbMATH DE number 2004965