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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Smooth extensions of Lipschitzian real functions


Author: Biagio Ricceri
Journal: Proc. Amer. Math. Soc. 104 (1988), 641-642
MSC: Primary 47H99; Secondary 54C20
MathSciNet review: 931749
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Abstract: In this short note we point out that any Lipschitzian real function $ f$ defined in a subset $ K$ of a Banach space $ E$, with $ \overline {{\text{span}}} {\text{(K)}} \ne {\text{E}}$, can be extended to a surjective, open and Lipschitzian real function $ g$ on $ E$ in such a way that, for every $ r \in {\mathbf{R}}$, the set $ {g^{ - 1}}(r)$ is arcwise connected. In fact, a more refined result is proved.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0931749-4
PII: S 0002-9939(1988)0931749-4
Article copyright: © Copyright 1988 American Mathematical Society