Completion Method And Stability Of Bounded Set In Normed Space

In 1911, Meissner firstly mentioned the concept of complete sets in article.Then, many mathematicians did a lot of important works around complete sets. But,until today, people still do not have a good knowledge of complete sets. In view of this situation, this paper will mainly research on methods of completion of sets and related questions in the stabilities of completion of sets.Firstly, this paper briefly reviews the origin and development of complete sets and the relevant concepts and properties related to complete sets. These basic knowledge will laid a solid foundation for the research work.In order to make readers have a deeper understanding of complete sets, some examples are provided in normed spaces, through these examples, we have a deep understanding of complete sets; once again, In view of the important role played by the condition(dc) in the completion of lower dimensional bounded closed sets in Banach spaces, a necessary condition as well as a sufficient condition for(dc) is provided, before proving this;sufficient condition, we did many jobs, concluding theorems and proposition. The sufficient condition improved two sufficient conditions for(dc) obtained by Papini and Senlin Wu. Finally, this paper researches on the stablities of spherical hull basing on the working of Schneider and gets a method which can get a completion of sets, this provides a new idea and method for the complete set.