Maximal Points of Convex Sets in Locally Convex Topological Vector Spaces: Generalization of the Arrow–Barankin–Blackwell Theorem

摘要: In 1953, Arrow, Barankin, and Blackwell proved that, if C is a nonempty compact convex set in Rn with its standard ordering, then the of points maximizing strictly positive linear functionals dense maximal C. this paper, we present generalization result. We show that locally topological space X K an ordering cone on such quasi-interiors dual K* are nonempty, For example, our work shows under appropriate conditions, density results hold spaces Rn, Lp(Ω, μ), 1≤p≤∞, lp, (Ω), Ω Hausdorff space, when they partially ordered their natural cones.