关于有效点集闭性的一个注记

A NOTE ON THE CLOSENESS OF THE SET OF EFFICIENT POINTS

本文证明了下面的结论:假设A是局部凸空间里的一个子集,C?A是满足尖条件的闭凸锥,对任意X∈A\E(A,C),假设都是F—点,则有效点集E(A,C)是闭的。

Let A be a subset in a locally convex space X and C be a closed convex cone withcusp condition. Denote by E(A,C) the set of efficient points of A?X with respect to C. It isproved that, under the assumption that all x∈A\E(A,C) are F-points of A, E (A, C) is anonempty closed set.