Azagra Rueda, Daniel (1997) Diffeomorphisms between spheres and hyperplanes in infinite-dimensional Banach spaces. Studia Mathematica, 125 (2). pp. 179-186. ISSN 0039-3223
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Official URL: http://journals.impan.gov.pl/sm/
Abstract
We prove that for every infinite-dimensional Banach space X with a Frechet differentiable norm, the sphere S-X is diffeomorphic to each closed hyperplane in X. We also prove that every infinite-dimensional Banach space Y having a (not necessarily equivalent) C-p norm (with p is an element of N boolean OR {infinity}) is C-p diffeomorphic to Y \ {0}.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Infinite-dimensional Banach space; Unit sphere; Hyperplane; Diffeomorphism |
| Subjects: | Sciences > Mathematics > Functions |
| ID Code: | 12280 |
| Deposited On: | 23 Feb 2011 11:43 |
| Last Modified: | 23 Feb 2011 11:43 |
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