On topological and linear homeomorphisms of certain function spaces
type: Item
instance of: scholarly article
title: On topological and linear homeomorphisms of certain function spaces
zbMATH Open document ID: 0676.54022
DOI: 10.1016/0166-8641(89)90033-3
author: Jan Baars
author: Jan van Mill
author: Jan Pelant
author: J. A. M. de Groot
published in: Topology and its Applications
publication date: 1989-01-01T00:00:00Z
review text: The main result of the paper is the following theorem: If X is a countable metric space which is not locally compact, then the function space \(C_ p(X)\) is homeomorphic to \(\sigma_{\omega}=(\ell^ 2_ f)^{\infty}\). A technical tool of the investigation of function spaces in the paper is the notion of Q-matrix due to J. van Mill. However the authors mentioned that the theorem follows from the result of \textit{T. Dobrowolski}, \textit{S. P. Gul'ko} and \textit{J. Mogilski} (submitted to Topology Appl.) on the topological equivalence \(C_ p(X)\approx \sigma_{\omega}\) for any countable metric nondiscrete space X. Two examples are given to show that function spaces \(C_ p(X)\) and \(C_ p(Y)\) need not be linearly homeomorphic for separable metric spaces X and Y which are not locally compact.
Mathematics Subject Classification ID: 54C35
Mathematics Subject Classification ID: 57N17
Mathematics Subject Classification ID: 57N20
zbMATH DE Number: 4107692
zbMATH Keywords: Hilbert cube
zbMATH Keywords: Z-subset
zbMATH Keywords: Q-matrix
reviewed by: Mikhail Tkachenko
MaRDI profile type: Publication
full work available at URL: 0166-8641(89)90033-3
OpenAlex ID: W1979629257
cites work: Q3672683
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Wikidata QID: Q127957000
description: scientific article; zbMATH DE number 4107692