向量优化中改进集的一些拓扑性质

Some Topological Properties of Improvement Sets in Vector Optimization

改进集是研究向量优化问题的一个十分重要的工具。首先证明了改进集的有关拓扑闭包和拓扑内部的一些性质。进一步,在改进集的条件下给出了拓扑向量空间中两个非空集合之和的拓扑内部与拓扑闭包的一些运算性质,并得到了它的一些等价刻画。最后给出了一些具体的例子对主要结果进行了解释。

Improvement sets are an important tool with which to study the vector optimization problems.In this paper,first some properties of topological closures and topological internal of the improvement set are proved.Furthermore,some operational characterizations of topological closures and topological internal of sum for two nonempty sets operations are presented by using improvement sets in topological vector space,and some equivalent characterizations are obtained.In addition,some examples are given to illustrate our main results.