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The range of the gradient of a continuously differentiable bump. (English) Zbl 0993.46023
The authors discuss a few properties of a smooth boundedly supported function on a Banach space in the spirit of the Darboux theorem and its generalization by Jan Malýr [Real Anal. Exch. 22, No. 1, 167-173 (1996; Zbl 0879.26042)].

MSC:
46G05 Derivatives of functions in infinite-dimensional spaces
58C20 Differentiation theory (Gateaux, Fréchet, etc.) on manifolds
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