向量优化中集合的一些拓扑与代数性质

Some Topological and Algebraic Properties of Sets in Vector Optimization

在假设B下,证明了int S(+F)=int S+F,建立了两个集合拓扑闭包相等与拓扑内部相等之间的等价条件。结合Flores-Bazán等人的思想,基于集合的代数闭包和代数内部提出了假设B1。在假设B1下,证明了cor S(+F)=cor S+F,得到了集合的代数闭包一定是代数闭集,代数内部一定是代数开集等结果。这些结果是对假设B下集合性质的进一步补充和拓展。

In this paper, int （S＋F） =int S4-F is proved under the assumption B. Moreover, we get equivalent conditions about two sets by the concepts of topological closure and topological interior. By means of the idea of Flores-Bazan et al, we present the assumption B1. Under the assumption B1, we obtain cor （S＋F） = cor S＋F. Based on the condition of assumption B1, we get that the algebraic closure is closed and algebraic interior is open and so on. These results extend and supplement various existing proper- ties of sets under assumption B2.