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