Category:Nests

This category contains results about Nests.
Definitions specific to this category can be found in Definitions/Nests.

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 $Y \subseteq X$