The Failure of Rolle's Theorem in Infini
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Daniel Azagra; Mar JimΓ©nez-Sevilla
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Article
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2001
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Elsevier Science
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English
β 171 KB
We prove the following new characterization of C p (Lipschitz) smoothness in Banach spaces. An infinite-dimensional Banach space X has a C p smooth (Lipschitz) bump function if and only if it has another C p smooth (Lipschitz) bump function f such that its derivative does not vanish at any point in