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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: maleva@wisdom.weizmann.ac.il
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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

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