Definition:Chain (Order Theory)/Subset Relation

Definition
Let $S$ be a set.

Let $\powerset S$ be its power set.

Let $N \subseteq \powerset S$ be a subset of $\powerset S$.

Then $N$ is a chain (of sets) :


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

Also known as
A chain (of sets) is also known as a nest, particularly in the wider context of class theory.

Also see

 * Definition:Nest
 * Definition:Chain (Order Theory)
 * Definition:Nested Sequence