Definition:Unit of System of Sets

Definition
Let $\mathcal S$ be a system of sets.

Let $U \in \mathcal S$ such that:
 * $\forall A \in \mathcal S: A \cap U = A$

Then $U$ is the unit of $\mathcal S$.

Note that, for a given system of sets, if $U$ exists then it is unique.