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

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.