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On the Lipschitz classification of normed spaces, unit balls, and spheres
| Content Provider | Semantic Scholar |
|---|---|
| Author | Nahum, Ronny |
| Copyright Year | 2001 |
| Abstract | For every normed space Z, we note its closed unit ball and unit sphere by Bz and Sz, respectively. Let X and Y be normed spaces such that Sx is Lipschitz homeomorphic to SXeR, and Sy is Lipschitz homeomorphic to SYeR. We prove that the following are equivalent: 1. X is Lipschitz homeomorphic to Y. 2. BX is Lipschitz homeomorphic to By. 3. SX is Lipschitz homeomorphic to Sy. This result holds also in the uniform category, except (2 or 3) => 1 which is known to be false. |
| Starting Page | 1995 |
| Ending Page | 1999 |
| Page Count | 5 |
| File Format | PDF HTM / HTML |
| DOI | 10.1090/S0002-9939-00-05782-8 |
| Volume Number | 129 |
| Alternate Webpage(s) | http://www.ams.org/journals/proc/2001-129-07/S0002-9939-00-05782-8/S0002-9939-00-05782-8.pdf |
| Alternate Webpage(s) | https://www.ams.org/journals/proc/2001-129-07/S0002-9939-00-05782-8/S0002-9939-00-05782-8.pdf |
| Alternate Webpage(s) | https://doi.org/10.1090/S0002-9939-00-05782-8 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
