TY - JOUR
T1 - Local properties of maps of the ball
AU - Kannai, Yakar
PY - 2003/1/30
Y1 - 2003/1/30
N2 - 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 B̄n 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.
AB - 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 B̄n 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.
UR - http://www.scopus.com/inward/record.url?scp=1842501933&partnerID=8YFLogxK
U2 - 10.1155/S1085337503204012
DO - 10.1155/S1085337503204012
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AN - SCOPUS:1842501933
SN - 1085-3375
VL - 2003
SP - 75
EP - 81
JO - Abstract and Applied Analysis
JF - Abstract and Applied Analysis
IS - 2
ER -