Definition:Nest
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Definition
Class Theory
Let $C$ be a class.
$C$ is a nest if and only if:
- $\forall x, y \in C: x \subseteq y$ or $y \subseteq x$
Chain of Sets
When the class in question is a set, the nest is usually referred to as a chain:
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 $Y \subseteq X$