Algebras of Cauchy continuous maps
type: Item
instance of: scholarly article
title: Algebras of Cauchy continuous maps
zbMATH Open document ID: 0549.54011
DOI: 10.1016/0022-247X(84)90004-0
author: Eva Colebunders
published in: Journal of Mathematical Analysis and Applications
publication date: 1984-01-01T00:00:00Z
review text: For \(F\subset R^ X\) a new Cauchy structure \(\gamma_ F\) on F is defined; it is coarser than the structure of uniform convergence (equal if F consists of bounded functions) and finer than the structure induced by the continuous convergence. It is proved that F is the set of all Cauchy-continuous maps on X with respect to a Cauchy structure on X iff F is a function algebra containing constants which is complete in \(\gamma_ F\). If F is a sublattice of \(R^ X\) containing constants, then the set of bounded functions from F is sequentially dense in \((F,\gamma_ F)\).
Mathematics Subject Classification ID: 54C35
Mathematics Subject Classification ID: 54E15
zbMATH DE Number: 3876173
zbMATH Keywords: complete function algebra
zbMATH Keywords: real-valued Cauchy continuous maps
zbMATH Keywords: Cauchy structure
zbMATH Keywords: uniform convergence
zbMATH Keywords: continuous convergence
reviewed by: M. Hušek
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3876173