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Local properties of maps of the ball

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  • Yakar Kannai

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.

Suggested Citation

  • Yakar Kannai, 2003. "Local properties of maps of the ball," Abstract and Applied Analysis, Hindawi, vol. 2003, pages 1-7, January.
    • Handle: RePEc:hin:jnlaaa:107103
    DOI: 10.1155/S1085337503204012
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