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)


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.


Banach Space Homogeneous Space Hyperbolic Space Solvable Group Polynomial Growth 
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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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