本质上是Banach空间闭凸子集的凸度量空间  

Convex Metric Spaces which Are Essentially Closed Convex Subsets of Banach Spaces

作　　者：旷华武 KUANG HUAWU(College of Mathematics and Statistics,Guizhou University,Guiyang 550025,China)

机构地区：[1]贵州大学数学与统计学院,贵阳550025

出　　处：《应用数学学报》2020年第4期728-741,共14页Acta Mathematicae Applicatae Sinica

摘　　要：利用凸度量空间中凸结构的性质,在保持凸组合关系与等距嵌入意义下,获得了一个凸度量空间本质上是某个Banach空间中闭凸子集的充分必要条件,并举例说明了其应用.By using the properties of convex structures in convex metric spaces,in the sense of preserving convex combination relation and isometric embedding,we obtain a sufficient and necessary condition for a convex metric space to be essentially a closed convex subset of a Banach space.Some examples are listed to illustrate our results.

关 键 词：凸度量空间 等距嵌入 BANACH空间 (闭)凸集 

分 类 号：O174.13[理学—数学] O177.2[理学—基础数学]