中文摘要：

为了研究实Banach空间中有界闭凸集有唯一完备化集的条件,总结了这一方面的已知结果。在此基础上,给出了Banach空间中有界闭凸集有唯一完备化集的几个充要条件和一个充分条件。拓展了（K,u）-完备集的定义,并讨论在实Banach空间中此概念与唯一完备化集的关系。

英文摘要：

In order to study the conditions for bounded closed and convex sets to have a unique completion in real Banach spaces,known results in this direction are summarized. Based on this,a sufficient condition as well as some necessary and sufficient conditions for bounded closed and convex sets to have a unique completion are provided. The notion of（ K,u）-completeness is extended,and the relation of this notion to the uniqueness of completion in real Banach spaces is discussed.