Metric betweenness, Ptolemaic spaces, and isometric embeddings of pretangent spaces in ℝ

被引：0

作者：

Bilet V.V. ^{[1
]}

Dovgoshey A.A. ^{[1
]}

机构：

[1] Institute of Applied Mathematics and Mechanics of the NAS of Ukraine, 74, R. Luxemburg Str.

来源：

Journal of Mathematical Sciences | 2012年 / 182卷 / 1期

关键词：

isometric embeddings; metric betweenness; Metric spaces; pretangent spaces; Ptolemaic spaces;

D O I：

10.1007/s10958-012-0726-2

中图分类号：

学科分类号：

摘要：

We study some properties of pretangent spaces describing the infinitesimal geometry of general metric spaces. The necessary and sufficient conditions characterizing Ptolemaic pretangent spaces and pretangent spaces, where every three points are situated "on a single straight line," are found. As a corollary, we obtain a criterion of embeddability of pretangent spaces into the set ℝ of real numbers endowed by the natural metric. © 2012 Springer Science+Business Media, Inc.

引用

页码：22 / 36

页数：14

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