Extreme points of convex compact sets in the Hilbert cube
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.
scientific article; zbMATH DE number 1053623
scientific article