序凸集与锥的正规性

Order-convex sets and normality of cones

研究了序凸集的一些运算性质，得到了紧序凸集的序端点表示定理．定理2紧序凸集是其所有序端点的序凸包．还利用序凸集给出了正规锥的两个特征性质．定理3实Banach空间E的锥P是正规的当且仅当E的任何有界集的序凸包是有界的．定理4实Banach空间E的锥P是正规的当且仅当E是局部序凸的，即E有一个序凸的零点邻域基．

Some operational properties are studied for the oeder-convex sets. The representation theorem with order-extremal points is obtained for compact order-convex sets. Using the order-convex sets, two characters are given for the normal cores. The main results areTheorem 2 Every compact order-convex set is identity with the order-convex hull of all its orderextremal points.Theorem 3 A cone P of real Banach space E is normal if and only if the order-convex hull of every bownded subset of E is boumded.Theorem 4 A cone P if a real Banach space E is normal of and only if E is locally order-convex,that is, E has a basis of order-convex neighbourhoods at zero.