Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-23T19:32:11.369Z Has data issue: false hasContentIssue false
  • English
  • Français

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]
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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