On convex cones with Schwarz-Zamfirescu property (Q1289333)

The author proves that most points of a typical compact convex subset of a locally compact infinite-dimensional metric one are extreme points. As usual, ``most'' means all except of those in a set of first Baire category, and by ``typical set'' we mean a set whose complement is a union of a countable family of nowhere dense sets. The presented theorem is analogical to the result of \textit{T. Schwarz} and \textit{T. Zamfirescu} [J. Austral. Math. Soc., Ser. A 43, 287-290 (1987; Zbl 0629.52002)].