Diffeomorphisms between spheres and hyperplanes in infinite-dimensional Banach spaces

Tom 125 / 1997

Daniel Azagra Studia Mathematica 125 (1997), 179-186 DOI: 10.4064/sm-125-2-179-186

Streszczenie

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 $Y \ {0}$.

Autorzy

  • Daniel Azagra

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