Function spaces homeomorphic to the countable product of \(\ell ^ f_ 2\)
type: Item
instance of: scholarly article
title: Function spaces homeomorphic to the countable product of \(\ell ^ f_ 2\)
zbMATH Open document ID: 0691.57009
DOI: 10.1016/0166-8641(90)90077-F
author: Jianyong Qiao
author: Sumit K. Garg
published in: Topology and its Applications
publication date: 1990-01-01T00:00:00Z
review text: Let \(C_ p(X)\) denote the space of continuous real-valued functions defined on a topological space X endowed with the pointwise convergence topology. Let \(C^*_ p(X)\) denote the linear subspace of \(C_ p(X)\) consisting of bounded functions. Let \(\ell^ f_ 2\) denote the subspace of the Hilbert space \(\ell^ 2\) consisting of all sequences for which all but finitely many terms are zero. The following is the main result of the paper: If X is a nondiscrete countable metric space, then each of \(C_ p(X)\) and \(C^*_ p(X)\) is homeomorphic to the countable infinite product \(\ell^ f_ 2\times \ell^ f_ 2\times... \).
reviewed by: Sukhjit Singh
Mathematics Subject Classification ID: 57N17
Mathematics Subject Classification ID: 57N20
Mathematics Subject Classification ID: 54C35
zbMATH DE Number: 4131277
zbMATH Keywords: absorbing set
zbMATH Keywords: strongly universal space
zbMATH Keywords: space of continuous real-valued functions
zbMATH Keywords: pointwise convergence topology
zbMATH Keywords: Hilbert space
zbMATH Keywords: nondiscrete countable metric space
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4131277