On the uniform density of \(C(X)\otimes C(Y)\) in \(C(X \times Y)\)
type: Item
instance of: scholarly article
title: On the uniform density of \(C(X)\otimes C(Y)\) in \(C(X \times Y)\)
zbMATH Open document ID: 1192.46004
DOI: 10.1016/S0019-3577(09)00015-9
author: P. D. Allenby
author: Coenraad C. A. Labuschagne
published in: Indagationes Mathematicae. New Series
publication date: 2009-12-07T00:00:00Z
review text: If \(X\) and \(Y\) are compact Hausdorff spaces, it is shown that every \(f \in C(X \times Y)_+\) can be approximated uniformly from below and above by elements of the form \(\sum_{i=1}^{i=n}f_ig_i\) where \(f_i\in C(X)_+\) and \(g_i\in C(Y)_+\) for \(i=1,\dots,n\). This result is then applied to the Fremlin tensor product of Archimedean Riesz spaces.
Mathematics Subject Classification ID: 46A40
Mathematics Subject Classification ID: 46B42
Mathematics Subject Classification ID: 06F20
zbMATH DE Number: 5643260
zbMATH Keywords: uniform convergence
zbMATH Keywords: space of continuous functions
reviewed by: Şafak Alpay
MaRDI profile type: Publication
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full work available at URL: s0019-3577(09)00015-9
OpenAlex ID: W2012103676
description: scientific article; zbMATH DE number 5643260