Uniform Non-Equivalence between Euclidean and Hyperbolic Spaces
| Autor: | E. Gorelik, J. Lindenstrauss, Mark Rudelson |
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| Rok vydání: | 1995 |
| Předmět: |
Pure mathematics
Mathematics::Dynamical Systems Eight-dimensional space Mathematics::General Mathematics Hyperbolic group Hyperbolic space Mathematics::General Topology Hyperbolic manifold Mathematics::Geometric Topology Relatively hyperbolic group Homeomorphism Uniform continuity Affine space Mathematics |
| Zdroj: | Geometric Aspects of Functional Analysis ISBN: 9783034899024 |
| DOI: | 10.1007/978-3-0348-9090-8_10 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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