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Uniform Non-Equivalence between Euclidean and Hyperbolic Spaces

  • E. Gorelik
  • J. Lindenstrauss
  • M. Rudelson
Conference paper
Part of the Operator Theory Advances and Applications book series (OT, volume 77)

Abstract

It is well known that the Euclidean and hyperbolic (Lobachevsky-Bolyai) spaces E n , H n of the same dimension n are homeomorphic. V. A. Efremovich ([1], [2]) proved in 1945, that E n and H n are not uniformly homeomorphic; this means that there does not exist any homeomorphism between them that is uniform together with its inverse.

Keywords

Banach Space Homogeneous Space Hyperbolic Space Solvable Group Polynomial Growth 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 1995

Authors and Affiliations

  • E. Gorelik
    • 1
  • J. Lindenstrauss
    • 2
  • M. Rudelson
    • 2
  1. 1.Bar Ilan UniversityIsrael
  2. 2.Institute of MathematicsThe Hebrew University of JerusalemJerusalemIsrael

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