Let $F:\mathbb{R}^2\to \mathbb{R}^2$ be a homogeneous function of degree $k\in \mathbb{Z}_+$ (i.e., $F(tx)=t^kF(x)$, $t>0$) such that $F^{-1}(\{0\}) = (0)$. It is true that F has topological degree less than or equal to k?
This is true if F is homogeneous polynomial!