Extreme Point Characterizations of Semi-Infinite Dual Non-Archimedean Balls

摘要

The extreme point characterization of the (l')-ball of a generalized finite sequence space by Kortanek and Strojwas was accomplished only for real scalars and by continuity considerations. This document shows that no topology of continuity is needed as in Kortanek-Strojwas and that the characterization extends to weighted (l')-balls with any ordered scalar field. A Chebyshev ball theorem is shown to be false since it has no extreme points. Via generalizing the LIEP, (Linear Independence with Extreme Points) theorem, useful projections of the ball are proved convex hulls of their extreme points. (Author)