Definition:Chain (Order Theory)/Subset Relation

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This page is about Chain of Sets in the context of Order Theory. For other uses, see Chain.

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) if and only if:

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

  • Results about chains can be found here.


Sources