Hyperstonean cover and second dual extension
type: Item
instance of: scholarly article
title: Hyperstonean cover and second dual extension
zbMATH Open document ID: 0667.54005
DOI: 10.1007/BF01903626
published in: Acta Mathematica Hungarica
publication date: 1988-01-01T00:00:00Z
review text: Let T be a completely regular space and \(C^*(T)\) denote the vector lattice of all bounded continuous real-valued functions on T. A vector lattice X is said to be an extension of \(C^*(T)\) in case there exists an injective vector lattice homomorphism from \(C^*(T)\) into X. Let \(C^*(T)'\) denote the vector lattice of all bounded Radon measures on T, and let \(C^*(T)''\) denote the vector lattice of all order-bounded functionals on \(C^*(T)'\). The author presents a purely topological construction of a completely regular space R that is the unique hyperstonian cover of T, starting from the Kelley ideals of T. Among his main results he shows that \(C^*(T)''\) and \(C^*(R)\) are isomorphic. He then derives various characterizations of \(C^*(T)''\) among all extensions of \(C^*(T)\).
Mathematics Subject Classification ID: 54C35
Mathematics Subject Classification ID: 46E05
zbMATH DE Number: 4092315
zbMATH Keywords: second dual space
zbMATH Keywords: vector-lattice extensions
zbMATH Keywords: C-ring extensions
zbMATH Keywords: hyperstonian cover
zbMATH Keywords: Kelley ideals
author: V. K. Zakharov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4092315