Publication: The hyperbolic dimension of metric spaces
The hyperbolic dimension of metric spaces
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Buyalo, S., & Schroeder, V. (2008). The hyperbolic dimension of metric spaces. St. Petersburg Mathematical Journal, 19(1), 67–76. https://doi.org/10.1090/S1061-0022-07-00986-7
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We introduce a new quasi-isometry invariant of metric spaces called the hyperbolic dimension, hypdim, which is a version of the Gromov's asymptotic dimension, asdim. The hyperbolic dimension is at most the asymptotic dimension, however, unlike the asymptotic dimension, the hyperbolic dimension of any Euclidean space R^n is zero (while asdim R^n=n.) This invariant possesses usual properties of dimension like monotonicity and product theorems. Our main result says that the hyperbolic dimension of any Gromov hyperbolic space X (with mild
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- Buyalo, S
- Schroeder, Viktor
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Buyalo, S., & Schroeder, V. (2008). The hyperbolic dimension of metric spaces. St. Petersburg Mathematical Journal, 19(1), 67–76. https://doi.org/10.1090/S1061-0022-07-00986-7
