Isometric embeddings of finite metric spaces

被引:1
|
作者
Oblakova, A. I. [1 ]
机构
[1] Moscow MV Lomonosov State Univ, Fac Mech & Math, Moscow 119991, Russia
关键词
D O I
10.3103/S0027132216010010
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
It is proved that there exists a metric on a Cantor set such that any finite metric space whose diameter does not exceed 1 and the number of points does not exceed n can be isometrically embedded into it. It is also proved that for any m, n a N there exists a Cantor set in R (m) that isometrically contains all finite metric spaces which can be embedded into R (m) , contain at most n points, and have the diameter at most 1. The latter result is proved for a wide class of metrics on R (m) and, in particular, for the Euclidean metric.
引用
收藏
页码:1 / 6
页数:6
相关论文
共 50 条