Abstract and Applied Analysis

Abstract and Applied Analysis / 2003 / Article

Open Access

Volume 2003 |Article ID 107103 | https://doi.org/10.1155/S1085337503204012

Yakar Kannai, "Local properties of maps of the ball", Abstract and Applied Analysis, vol. 2003, Article ID 107103, 7 pages, 2003. https://doi.org/10.1155/S1085337503204012

Local properties of maps of the ball

Received25 Jan 2002


Let f be an essential map of Sn1 into itself (i.e., f is not homotopic to a constant mapping) admitting an extension mapping the closed unit ball B¯n into n. Then, for every interior point y of Bn, there exists a point x in f1(y) such that the image of no neighborhood of x is contained in a coordinate half space with y on its boundary. Under additional conditions, the image of a neighborhood of x covers a neighborhood of y. Differential versions are valid for quasianalytic functions. These results are motivated by game-theoretic considerations.

Copyright © 2003 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.

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