HYPERBOLIC DIMENSION OF METRIC SPACES

@inproceedings{BUYALO2007HYPERBOLICDO,
  title={HYPERBOLIC DIMENSION OF METRIC SPACES},
  author={S. BUYALO},
  year={2007}
}
  • S. BUYALO
  • Published 2007
A new quasi-isometry invariant of metric spaces, called the hyperbolic dimension (hypdim) is introduced; this is a version of Gromov’s asymptotic dimension (asdim). The inequality hypdim ≤ asdim is always fulfilled; however, unlike the asymptotic dimension, hypdim Rn = 0 for every Euclidean space Rn (while asdim Rn = n). This invariant possesses the usual properties of dimension such as monotonicity and product theorems. The main result says that the hyperbolic dimension of any Gromov… CONTINUE READING

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