ON THE ASSOUAD DIMENSION AND CONVERGENCE OF METRIC SPACES

被引：0

作者：

Ishiki, Yoshito ^{[1
]}

机构：

[1] Univ Tsukuba, Grad Sch Pure & Appl Sci, Tennodai 1-1-1, Tsukuba, Ibaraki 3058571, Japan

来源：

KODAI MATHEMATICAL JOURNAL | 2020年 / 43卷 / 03期

关键词：

Assouad dimesnion; Gromov-Hausdorff convergence; ASYMPTOTIC CONES;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce the notion of pseudo-cones of metric spaces as a generalization of both of the tangent cones and the asymptotic cones. We prove that the Assouad dimension of a metric space is bounded from below by that of any pseudo-cone of it. We exhibit an example containing all compact metric spaces as pseudo-cones, and examples containing all proper length spaces as tangent cones or asymptotic cones.

引用

页码：573 / 590

页数：18

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