Abstract and Applied Analysis

Local properties of maps of the ball

Yakar Kannai

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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.

Article information

Abstr. Appl. Anal., Volume 2003, Number 2 (2003), 75-81.

First available in Project Euclid: 15 April 2003

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 26E10: $C^\infty$-functions, quasi-analytic functions [See also 58C25] 58K05
Secondary: 55M25 47H10 47H11 57N75 57Q65


Kannai, Yakar. Local properties of maps of the ball. Abstr. Appl. Anal. 2003 (2003), no. 2, 75--81. doi:10.1155/S1085337503204012. https://projecteuclid.org/euclid.aaa/1050426052

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