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

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

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.