Let $F$ be a foliation of a smooth manifold $M$. The fundamental groupoid $\Pi(F)$ of $F$ is the set
$\Pi(F)=\frac{\{\alpha:[0,1]\to M\text{ path cointained in a leaf}\}}{\text{homotopy with fixed end points }}$.
I can't see why the fundamental groupoid of the foliation of $\mathbb{R}^3\setminus\{0\}$ by horizontal planes is not Hausdorff. Any help would be welcomed :)