关于有效点集的闭性和连通性

On the Closeness and Connectedness of the Set of Efficient Points

中文关键词:  有效点集  F-集  连通集

中文摘要:

      本文的主要结果是，假设Ａ是局部凸空间里的紧的Ｆ一集，则Ａ的有效点集Ｅ（Ａ｜Ｃ）是闭集。需要提及的是，此结果中关于Ａ并没有作任何凸性的假设，如果对它再附加某种凸性假设条件时，则本文进一步证明了有效点集Ｅ（Ａ｜Ｃ）不但是闭集，而且还是连通集。

英文摘要:

      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 the set A with respect toC. Suppose that A is a compact F-set not necessarily convex。We obtain some resultson the closeness of the set of efficient points。Furthermore,we prove that under someadequate convex assurnptions the set S(A\C)is connected.