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Abstract. In this paper we present a
condition for a polynomial map F:= (f1, f2,
..., fn): Rn
--->Rn to be a
global polynomial diffeomorphism. To do this we express a sufficient
condition in terms of the Newton
polyhedron for a polynomial function f: Rn
---> R to be a proper map. We also prove that the fiber f
-1(A), with large value |A|, of a proper polynomial f
is diffeomorphic to the unit sphere Sn-1,
if it is non-empty.
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