Let $H=(V,E)$ be a hypergraph such that $\bigcup E = V$. For $D\subseteq V$ we set $N_D = \bigcup\{e\in E: D\cap e\neq \emptyset\}$. We say that $D\subseteq V$ is *dominating* if $N_D = V$.

Hypergraphs need not have minimal dominating sets with respect to $\subseteq$.

But: Is every non-dominating set contained in a non-dominating set that is maximal with repect to $\subseteq$?