Smooth extensions of Lipschitzian real functions
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- by Biagio Ricceri PDF
- Proc. Amer. Math. Soc. 104 (1988), 641-642 Request permission
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.References
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Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 104 (1988), 641-642
- MSC: Primary 47H99; Secondary 54C20
- DOI: https://doi.org/10.1090/S0002-9939-1988-0931749-4
- MathSciNet review: 931749