On a Lipschitz invariant of normed spaces
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- by Yoav Benyamini PDF
- Proc. Amer. Math. Soc. 110 (1990), 979-981 Request permission
Abstract:
C. Bessaga introduced an invariant $\eta (X)$ for $\sigma$-compact normed linear spaces. He showed that $\eta (X) = \eta (Y)$ whenever $X$ and $Y$ are Lipschitz homeomorphic. In this note we construct two $\sigma$-compact normed spaces with $\eta (X) = \eta (Y)$ which are not Lipschitz homeomorphic. Moreover, there are no compact convex sets $K$ and $L$ generating $X$ and $Y$, respectively, which are Lipschitz homeomorphic. This answers two problems posed by Bessaga.References
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- C. Bessaga, A Lipschitz invariant of normed linear spaces related to the entropy numbers, Rocky Mountain J. Math. 10 (1980), no. 1, 81–84. MR 573863, DOI 10.1216/RMJ-1980-10-1-81
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- Piotr Mankiewicz, On the differentiability of Lipschitz mappings in Fréchet spaces, Studia Math. 45 (1973), 15–29. MR 331055, DOI 10.4064/sm-45-1-15-29
Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 110 (1990), 979-981
- MSC: Primary 46B20
- DOI: https://doi.org/10.1090/S0002-9939-1990-1028040-6
- MathSciNet review: 1028040