CONVEX-COMPACT SETS AND BANACH DISCS

摘要

Every relatively convex-compact convex subset of a locally convex space iscontained in a Banach disc. Moreover, an upper bound for the class of sets which arecontained in a Banach disc is presented. If the topological dual E' of a locally convex spaceE is the o-(E', E)-closure of the union of countably many σ(E' ,E)-relatively countablycompacts sets, then every weakly (relatively) convex-compact set is weakly (relatively)compact.