Definition:Chain (Order Theory)/Subset Relation

Definition
Let $S$ be a set, and let $\mathcal P \left({S}\right)$ be its power set.

Let $N \subseteq \mathcal P \left({S}\right)$ be a subset of $\mathcal P \left({S}\right)$.

Then $N$ is a nest :


 * $\forall X, Y \in N: X \subseteq Y$ or $Y \subseteq X$

Also see

 * Chain


 * Nest under Subset Ordering is Chain