有限表示和树性质是研究超性质的重要工具,James利用有限树和有限表示定理给出了超自反空间的重要特征.在研究超自反空间和再赋范问题时,树性质成为行之有效的研究工具.本文引入了可分有限树的概念并利用Banaeh空间中两个集合之间的有限表示的概念,讨论了完备连续性质和具有超完备连续性质的非空有界闭凸集的性质,给出了超完备连续性质的一个局部特征,并且用可分有限树刻划了具有超完备连续性质的Banaeh空间.
Finite representation and tree-property are important for study on super-property. James characterized super-reflexive space by finite tree. Finite representation and tree-property are also very important for the research about super-reflexive space and renorming. This paper introduces a notion of separated finite tree and in terms of finite representation between two sets. The paper gives a local characterization of super complete continuity property. Furthermore, the paper gives a characterization of the Banach space which has super complete continuity property.