中文摘要：

研究了Banach空间X中的有界闭凸集C的弱紧性与其可逼近性的关系，证明了C是弱紧的当且仅当C在每个包含它（在仿射等距的意义下）的Banach空间中均是可逼近的．而当C不是完全时，C是弱紧的当且仅当对于x的每个等价范数｜·｜，C在（X，｜·｜）中均是可逼近的．

英文摘要：

We investigate the relationship between the weakly compactness and the proximinality of a bounded closed convex set C in a Banach space X. We prove that C is weakly compact if and only if C is proximinal in every Banach space which contains it （in the sense of affine isometry）. And when C is not total,we show that C is weakly compact if and only if for every equivalent norm ｜·｜ on X,C is proximinal in （X, ｜·｜ ）.