Foliations and global injectivity in ℝ.

Let F: ℝ → ℝ be a polynomial local diffeomorphism and let S denote the set of not proper points of F. The Jelonek's real Jacobian Conjecture states that if codim( S) ≥ 2, then F is bijective. We prove a weak version of such conjecture establishing the sufficiency of a necessary condition for the bijectivity of F. [ABSTRACT FROM AUTHOR]