Convex compact spaces and their maps

AbstractThe relation of the topological properties of convex compact subsets of locally convex spaces and those of the sets of their extreme points is examined. The principal question studied is whether the weight of a convex compact space and the weight of the set of its extreme points coincide. It is proved that if K is a convex compact space and E is the set of its extreme points, then w(E) = nw(E) = L(E) · Δ(E),w(K) = w(E) · hL(K). If E is a Lindelöf space or K is a simplex, then w(K) = w(E)