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Metric space inversions, quasihyperbolic distance, and uniform spaces |
Buckley, Stephen M.; Herron, David A.; Xie, Xiangdong
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We 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.
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Keyword(s):
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Mathematics; Inversion; Sphericalization; Quasimöbius; Quasihyperbolic metric; Uniform space. |
Publication Date:
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2008 |
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Type:
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Journal article |
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Peer-Reviewed:
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No |
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Institution:
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NUI Maynooth |
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Citation(s):
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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 |
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Publisher(s):
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Department of Mathematics Indiana University |
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File Format(s):
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application/pdf |
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Related Link(s):
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http://eprints.nuim.ie/1610/1/BuckleyMetricSpace.pdf |
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First Indexed:
2009-11-06 02:00:15 Last Updated:
2012-05-17 05:06:02 |
