Characterization of separable metric R-trees
Characterization of separable metric R-trees
复制标题
可分离度量 R 树的表征
DOI：
10.1090/s0002-9939-1992-1124147-5
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发表时间：
1992
期刊：
影响因子：
--
通讯作者：
E. Tymchatyn
中科院分区：
文献类型：
--
作者：
J. Mayer;L. Mohler;L. Oversteegen;E. Tymchatyn
R-树(X，d)是一个唯一的弧形连通度量空间，其中每条弧都等距于实数的子弧。R-树是在研究双曲空间等距群时自然产生的。其中两位作者以前在度量空间中对R-树进行了拓扑学刻画。本文的目的是为可分度量空间的这一刻划提供一个更简单的证明。主要定理如下：设(X，r)是可分度量空间。则下列条件是等价的：(1)X有一个等价的度量d使得(X，d)是R-树。(2)X是局部弧连通的，且是唯一弧连通的
An R-tree (X, d) is a uniquely arcwise connected metric space in which each arc is isometric to a subarc of the reals. R-trees arise naturally in the study of groups of isometries of hyperbolic space. Two of the authors had previously characterized R-trees topologically among metric spaces. The purpose of this paper is to provide a simpler proof of this characterization for separable metric spaces. The main theorem is the following : Let (X, r) be a separable metric space. Then the following are equivalent : (1) X admits an equivalent metric d such that (X, d) is an R-tree. (2) X is locally arcwise connected and uniquely arcwise connected