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Abstract and Applied Analysis
Volume 2005 (2005), Issue 5, Pages 543-562
http://dx.doi.org/10.1155/AAA.2005.543

On Lipschitz ball noncollapsing functions and uniform co-Lipschitz mappings of the plane

1Department of Mathematics, Weizmann Institute of Science, Rehovot 76100, Israel
2Department of Mathematics, University College London, Gower Street, London WC1E 6BT, United Kingdom

Received 29 October 2003

Copyright © 2005 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We give a sharp estimate on the cardinality of point preimages of a uniform co-Lipschitz mapping on the plane. We also give a necessary and sufficient condition for a ball noncollapsing Lipschitz function to have a point with infinite preimage.