Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2003, Number 2 (2003), 75-81.
Local properties of maps of the ball
Let be an essential map of into itself (i.e., is not homotopic to a constant mapping) admitting an extension mapping the closed unit ball into . Then, for every interior point of , there exists a point in such that the image of no neighborhood of is contained in a coordinate half space with on its boundary. Under additional conditions, the image of a neighborhood of covers a neighborhood of . Differential versions are valid for quasianalytic functions. These results are motivated by game-theoretic considerations.
Abstr. Appl. Anal., Volume 2003, Number 2 (2003), 75-81.
First available in Project Euclid: 15 April 2003
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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