Publication: Diffeomorphisms between spheres and hyperplanes in infinite-dimensional Banach spaces
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1997
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Polish Acad Sciencies Inst Mathematics
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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}.