Local Properties of Maps of the Ball

نویسنده

  • YAKAR KANNAI
چکیده

Let f be an essential map of Sn−1 into itself (i.e., f is not homotopic to a constant mapping) admitting an extension mapping the closed unit ball B n into Rn. Then, for every interior point y of Bn, 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.

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تاریخ انتشار 2002