# Category:Nests

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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 $Y \subseteq X$

## Subcategories

This category has the following 5 subcategories, out of 5 total.

## Pages in category "Nests"

The following 8 pages are in this category, out of 8 total.