Local properties of maps of the ball

Yakar Kannai

Abstract and Applied Analysis, 2003, vol. 2003, 1-7

Abstract:

Let f be an essential map of S n − 1 into itself (i.e., f is not homotopic to a constant mapping) admitting an extension mapping the closed unit ball B ¯ n into ℝ n . Then, for every interior point y of B n , there exists a point x in f − 1 ( 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.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:107103

DOI: 10.1155/S1085337503204012

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