Let $H=(V,E)$ be a hypergraph. We call it Hausdorff if for all $x\neq y \in V$ there are $e_1,e_2\in E$ with $e_1\cap e_2 = \emptyset$ such that $x\in e_1$ and $y\in e_2$.

If $H=(V,E)$ is a Hausdorff hypergraph, is it possible that $|E|<|V|$?