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30 January 2003 Local properties of maps of the ball
Yakar Kannai
Abstr. Appl. Anal. 2003(2): 75-81 (30 January 2003). DOI: 10.1155/S1085337503204012


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.


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Yakar Kannai. "Local properties of maps of the ball." Abstr. Appl. Anal. 2003 (2) 75 - 81, 30 January 2003.


Published: 30 January 2003
First available in Project Euclid: 15 April 2003

zbMATH: 1017.26020
MathSciNet: MR1960138
Digital Object Identifier: 10.1155/S1085337503204012

Primary: 26E10 , 58K05
Secondary: 47H10 , 47H11 , 55M25 , 57N75 , 57Q65

Rights: Copyright © 2003 Hindawi

Vol.2003 • No. 2 • 30 January 2003
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