The Stone--Weierstrass theorem and spaces of measures
type: Item
instance of: scholarly article
title: The Stone--Weierstrass theorem and spaces of measures
zbMATH Open document ID: 1027.54023
DOI: 10.1023/A:1020511807357
author: V. P. Fedorova
published in: Mathematical Notes
publication date: 2003-06-15T00:00:00Z
review text: The classical Stone-Weierstrass theorem says: if \(X\) is a compact topological space and a subalgebra in the algebra \(C(X)\) of all real-valued continuous functions on \(X\) contains constants and separates points of \(X\), then this subalgebra is dense in \(C(X)\) with respect to the topology of uniform convergence on \(X\). Here the author considers the lattice form of this theorem, that is the vector lattice \(C_b(X)\), where \(X\) is a completely regular space, is considered with locally convex topologies \(t\) for which \((C_b(X),t)'\) is a space of \(\tau\)-additive functionals. For some classes of \(X\), the author proves analogs of the Stone-Weierstrass theorem.
Mathematics Subject Classification ID: 54C35
zbMATH DE Number: 1928301
zbMATH Keywords: Stone-Weierstrass theorem
zbMATH Keywords: regular space
zbMATH Keywords: locally convex topologies
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: a:1020511807357
OpenAlex ID: W128109922
description: scientific article; zbMATH DE number 1928301