Order arc

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A collection $\mathcal{N}$ is called a nest if for any pair $N_1,N_2 \in \mathcal{N}$, either $N_1 \subset N_2$ or $N_2 \subset N_1$. Let $H$ be a subset of the hyperspace $2^X$. An order arc in $H$ is an arc $\alpha$ in $H$ such that $\alpha$ is a nest.