There
are obtained conditions under which maps from $\R^n$ to itself are
globally injective. In particular there are proved some partial
results related to the Weak Markus-Yamabe Conjecture which states
that if a vector field $X:\R^n \to \R^n$ has the property that,
for all $p\in\R^n$, all the eigenvalues of $DX(p)$ have negative
real part, then $X$ has at most one singularity.