From: David G Radcliffe <radcliff@alpha2.csd.uwm.edu>
Subject: Re: Polynomial mapping of R^d
Date: 3 Jan 2001 05:39:58 GMT
Newsgroups: sci.math
Summary: One-to-one polynomial maps are onto

tim_brooks@my-deja.com wrote:
: If d >= 1 and T is a polynomial mapping from R^d -> R^d
: i,e T = (P1,P2,...Pd) with P1,P2,..Pd polynomials in x1,x2,...xd and T
: is 1 to 1 on R^d ,does it follwos that T is onto R^d ?

: Tim

Yes. The result is proved in
A. Bialynicki-Birula and M. Rosenlicht, Injective morphisms of real 
algebraic varieties, Proc. AMS 13 (1962), pp.200-203.