The range of the derivative of a differentiable bumpL'image de la dérivée d'une fonction bosse différentiable |
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Authors: | Thierry Gaspari |
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Institution: | Mathématiques pures de Bordeaux (MPB), UMR 5467 CNRS, Université Bordeaux 1, 351, cours de la Libération, 33405 Talence cedex, France |
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Abstract: | We study the range of the derivative of a Frechet differentiable bump. X is an infinite dimensional separable Cp-smooth Banach space. We first prove that any connected open subset of containing 0 is the range of the derivative of a Cp-bump. Next, analytic subsets of which satisfy a natural linkage condition are the range of the derivative of a C1-bump. We find analogues of these results in finite dimensions. We finally show that is the closure of its interior, if f is a C2-bump on . To cite this article: T. Gaspari, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 189–194. |
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