CARDINALITY OF SOME CONVEX SETS AND OF THEIR SETS OF EXTREME POINTS

We show that the cardinality n of a compact convex set W in a topological linear space X satisfies the condition that n(aleph 0) = n. We also establish some relations between the cardinality of W and that of extr W provided X is locally convex. Moreover, we deal with the cardinality of the convex set E(mu) of all quasi-measure extensions of a quasi-measure mu, defined on an algebra of sets, to a larger algebra of sets, and relate it to the cardinality of extr E(mu).