Metric space inversions, quasihyperbolic distance, and uniform spaces
Metric space inversions, quasihyperbolic distance, and uniform spaces
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DOI：
10.1512/iumj.2008.57.3193
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发表时间：
2008
影响因子：
1.1
通讯作者：
S. Buckley;D. Herron;Xiangdong Xie
中科院分区：
文献类型：
--
作者：
S. Buckley;D. Herron;Xiangdong Xie
我们定义了在一般度量空间中有效的逆的概念。我们建立了几个关于逆的基本事实；例如，它们是拟双曲的同态和拟双曲的bilipschitz。在某种意义上，反转是球化的双重性质。我们证明了反转和球化都保持了局部拟凸性和环状拟凸性以及一致性。
We define a notion of inversion valid in the general metric space setting. We establish several basic facts concerning inversions; e.g., they are quasimobius homeomorphisms and quasihyperbolically bilipschitz. In a certain sense, inversion is dual to sphericalization. We demonstrate that both inversion and sphericalization preserve local quasiconvexity and annular quasiconvexity as well as uniformity.