Geodesic
Diffeomorphisms between spheres and hyperplanes in infinite-dimensional Banach spaces
Studia Mathematica, Tome 125 (1997) no. 2, pp. 179-186

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We prove that for every infinite-dimensional Banach space X with a Fréchet 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 $p ∈ ℕ ∪ {∞}$)$ is $C^p$ diffeomorphic to $Y \ {0}$.
DOI : 10.4064/sm-125-2-179-186
Keywords: $C^p$ smooth norm, spheres and hyperplanes in Banach spaces

Daniel Azagra 1

1 
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Daniel Azagra. Diffeomorphisms between spheres and hyperplanes in infinite-dimensional Banach spaces. Studia Mathematica, Tome 125 (1997) no. 2, pp. 179-186. doi: 10.4064/sm-125-2-179-186

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