Local properties of maps of the ball

Yakar Kannai

Abstract and Applied Analysis, 2003, vol. 2003, issue 2, 75-81

Abstract: 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.

Date: 2003
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/S1085337503204012

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2003:y:2003:i:2:p:75-81

Access Statistics for this article

More articles in Abstract and Applied Analysis from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().