中文摘要：

改进集是研究向量优化问题十分重要的工具之一。基于改进集对偶锥和回收锥的一些基本性质在适当假设条件下证明了对于有限维空间Rn中两个闭集E1,E2,若cl（cone（convE1））是点的,则E1,E2之和E1＋E2仍为闭集。并提出了一些具体例子对主要结果进行了解释,指出若cl（cone（conv E1））不是点的,其结论不一定成立。

英文摘要：

Improvement set is one of the most important tools to study vector optimization problems. In this paper, by some basic dual characterizations of improvement sets and some tools including as recession cone, the closedness of a sum of two closed sets E1 and E2 is proved if cl（cone（conv E1 ）） is pointed under some suitable assumption conditions in finite dimensional space R＂. Moreo- ver, some concrete examples also are presented to illustrate the main results and show that the closedness of a sum of two closed sets may be invalid if cl（cone（conv El ）） is not pointed.