1995•Birkhäuser Basel eBooksRequires access
Uniform Non-Equivalence between Euclidean and Hyperbolic Spaces
E. Gorelik, Joram Lindenstrauss, Mark Rudelson
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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.