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2013 Hyperbolic construction of Cantor sets
Zair Ibragimov, John Simanyi
Involve 6(3): 333-343 (2013). DOI: 10.2140/involve.2013.6.333

Abstract

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.

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Zair Ibragimov. John Simanyi. "Hyperbolic construction of Cantor sets." Involve 6 (3) 333 - 343, 2013. https://doi.org/10.2140/involve.2013.6.333

Information

Received: 6 July 2012; Revised: 21 December 2012; Accepted: 6 January 2013; Published: 2013
First available in Project Euclid: 20 December 2017

zbMATH: 06227501
MathSciNet: MR3101765
Digital Object Identifier: 10.2140/involve.2013.6.333

Subjects:
Primary: 30C65
Secondary: 05C25

Keywords: Cantor set , Gromov hyperbolic spaces

Rights: Copyright © 2013 Mathematical Sciences Publishers

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Vol.6 • No. 3 • 2013
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