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Hyperbolic
construction of Cantor sets
Zair Ibragimov and John Simanyi
Vol. 6 (2013), No. 3, 333–343
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Abstract |
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In this paper we present a new construction of the ternary Cantor set within the context of Gromov hyperbolic geometry. Unlike the standard construction, where one proceeds by removing middle-third intervals, our construction uses the collection of the removed intervals. More precisely, we first hyperbolize (in the sense of Gromov) the collection of the removed middle-third open intervals, then we define a visual metric on its boundary at infinity and then we show that the resulting metric space is isometric to the Cantor set. |
Keywords
Cantor set, Gromov hyperbolic spaces
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Mathematical Subject Classification 2010
Primary: 30C65
Secondary: 05C25
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Milestones
Received: 6 July 2012
Revised: 21 December 2012
Accepted: 6 January 2013
Published: 8 September 2013
Communicated by Kenneth S. Berenhaut
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Authors |
| Zair Ibragimov | |
| Department of Mathematics California State University, Fullerton McCarthy Hall 154 Fullerton, CA 92831 United States |
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| John Simanyi | |
| Department of Mathematics California State University, Fullerton McCarthy Hall 154 Fullerton, CA 92831 United States |
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