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


On a Lipschitz invariant of normed spaces

Author: Yoav Benyamini
Journal: Proc. Amer. Math. Soc. 110 (1990), 979-981
MSC: Primary 46B20
MathSciNet review: 1028040
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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.

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PII: S 0002-9939(1990)1028040-6
Article copyright: © Copyright 1990 American Mathematical Society