FINITE METRIC-SPACES NEEDING HIGH DIMENSION FOR LIPSCHITZ EMBEDDINGS IN BANACH-SPACES

被引：10

作者：

ARIASDEREYNA, J

RODRIGUEZPIAZZA, L

机构：

[1] Departmento de Análisis Matemático, Universidad de Sevilla, Sevilla, 41080

来源：

ISRAEL JOURNAL OF MATHEMATICS | 1992年 / 79卷 / 01期

关键词：

D O I：

10.1007/BF02764804

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct a sequence of metric spaces (M(n)) with card M(n) = n satisfying that for every c < 2, there exists a real number a(c) > 0 such that, if the Lipschitz distance from M(n) to a subset of a Banach space E is less than c, then dim(E) greater-than-or-equal-to a(c)n. We also prove several results about embeddings of metric spaces whose non-zero distance values are in the interval [1,2].

引用

页码：103 / 111

页数：9