  In this work we present a new polynomial map $f:=(f_1,f_2):{\mathbb
R}^2\to{\mathbb R}^2$ whose image is the open quadrant
$\{x>0,y>0\}\subset{\mathbb R}^2$. The proof of this fact involves arguments of
topological nature that avoid hard computer calculations. In addition each
polynomial $f_i\in{\mathbb R}[{\tt x},{\tt y}]$ has degree $\leq16$ and only
$11$ monomials, becoming the simplest known map solving the open quadrant
problem.
