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Lipschitz quotient mappings with good ratio of constants

Part of: Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  26 February 2010

Olga Maleva
Olga Maleva
Affiliation:
Department of Mathematics, The Weizmann Institute of Science, Rehovot 76100, Israel, E-mail: [email protected]
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Abstract

It is shown that Lipschitz quotient mappings between finite dimensional spaces behave nicely (e.g., are bijective in the case of equal dimensions) if the Lipschitz and co-Lipschitz constants are close to each other. For Lipschitz quotient mappings of the plane, a bound for the cardinality of the pre-image of a point in terms of the ratio of the constants is obtained.

MSC classification

Secondary: 46B20: Geometry and structure of normed linear spaces
Type
Research Article
Information
Mathematika , Volume 49 , Issue 1-2 , June 2002 , pp. 159 - 165
Copyright
Copyright © University College London 2002

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References

[C]Csörnyei, M.. Can one squash the space into the plane without squashing?, Geom. Fund. Analysis 11 (2001), 933–952.Google Scholar
[JLPS]Johnson, W. B., Lindenstrauss, J., Preiss, D., and Schechtman, G.. Uniform quotient mappings of the plane, Michigan Math. J. 47 (2000), 15–31.CrossRefGoogle Scholar
[MU]Mazur, S., Ulam, S.. Sur les transformations isométriques d'espaces vectoriels normés, C.R. Acad. Sci. Paris 194 (1932), 946–948.Google Scholar