Metric space inversions, quasihyperbolic distance, and uniform spaces
Buckley, Stephen M. and Herron, David A. and Xie, Xiangdong (2008) Metric space inversions, quasihyperbolic distance, and uniform spaces. Indiana University Mathematics Journal, 57 (2). pp. 837-890. ISSN 0022-2518 AbstractWe dene a notion of inversion valid in the general metric space setting. We establish several basic facts concerning inversions; e.g., they are quasimöbius 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. | Keywords: | Inversion; Sphericalization; Quasimöbius; Quasihyperbolic metric; Uniform space. |
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| Subjects: | Science & Engineering > Mathematics |
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| ID Code: | 1610 |
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| Deposited By: | Prof. Stephen Buckley |
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| Deposited On: | 21 Oct 2009 10:38 |
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| Journal or Publication Title: | Indiana University Mathematics Journal |
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| Publisher: | Department of Mathematics Indiana University |
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| Refereed: | No |
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| URL: | http://www.iumj.indiana.edu/ |
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