The topological space of all extreme points of a compact convex set

G. Choquet and R. Haydon have proved that every Polish (i.e. completely metrizable and separable) spaceX is homeomorphic to the space of all extreme points of a metrizable compact convex setK which can be chosen to be even a Choquet simplex. In our paper we generalize partially this result to the case of a complete metric spaceX of zero covering dimension, without requiring any separability property forX.