Dual spaces of \(C_{\infty}(X)\)
type: Item
instance of: scholarly article
title: Dual spaces of \(C_{\infty}(X)\)
zbMATH Open document ID: 0617.46031
DOI: 10.1007/BF02844048
author: Wolfgang Filter
publication date: 1986-01-01T00:00:00Z
review text: Characterizations of the important dual spaces of the Riesz space \(C_{\infty}(X)\) of extended-real-valued continuous functions with dense set of points of finiteness on some locally compact Stonian space X are given. In particular, the extended order dual of \(C_{\infty}(X)\) (introduced by Luxemburg and Masterson) can be described as an inductive limit of Riesz spaces of normal Radon measures, which can even be identified with \(C_{\infty}(X)\) if X is hyperstonian.
Mathematics Subject Classification ID: 46E05
Mathematics Subject Classification ID: 46A40
zbMATH DE Number: 4000737
zbMATH Keywords: Riesz space
zbMATH Keywords: dense set of points of finiteness
zbMATH Keywords: locally compact Stonian space
zbMATH Keywords: extended order dual
zbMATH Keywords: inductive limit of Riesz spaces of normal Radon measures
zbMATH Keywords: hyperstonian
MaRDI profile type: Publication
cites work: Q4186829
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published in: Rendiconti del Circolo Matematico di Palermo
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description: scientific article; zbMATH DE number 4000737