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Diffeomorphisms between spheres and hyperplanes in infinite-dimensional Banach spaces

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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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 10:43
Last Modified:06 Feb 2014 09:21

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