Extreme points of convex compact sets in the Hilbert cube
type: Item
instance of: scholarly article
title: Extreme points of convex compact sets in the Hilbert cube
zbMATH Open document ID: 0882.46003
DOI: 10.1007/BF02509621
publication date: 1997-11-05T00:00:00Z
review text: The author proves extreme point results for compact convex sets in the Hilbert cube \(H\): If \(M\subseteq K\) is a \(G_\delta\)-subset of a metric compact \(K\), there is a continuous map \(\varepsilon:K\to H\) such that \(\text{ext conv }\varepsilon(K)=\varepsilon(M)\) and \(\varepsilon|_M\) is a topological imbedding. If \(M\subseteq K\) is dense and \(K\setminus M\) is weakly countable-dimensional, there is a topological imbedding \(\varepsilon:K\to M\) such that \(\text{ext conv }\varepsilon(K)=\varepsilon(M)\). The results are of interest in connection with Choquet's representation theorem.
Mathematics Subject Classification ID: 46A55
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 52A07
Mathematics Subject Classification ID: 46C05
zbMATH DE Number: 1053623
zbMATH Keywords: extreme point
zbMATH Keywords: compact convex sets
zbMATH Keywords: Hilbert cube
zbMATH Keywords: topological imbedding
zbMATH Keywords: Choquet's representation theorem
author: Efim M. Bronshteĭn
MaRDI profile type: Publication
cites work: Extreme point properties of convex bodies in reflexive Banach spaces
cites work: Extreme boundaries of convex bodies in \(\ell_2\)
cites work: A New Proof that every Polish Space is the Extreme Boundary of a Simplex
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published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 1053623