Closure

Definition: Closure

Let $S$ be a set with an $n$-ary operation $o:\underset{n\text{ times}}{\underbrace{S\times \cdots \times S}}\to S$.

We say that a subset $C\subseteq S$ is closed under $o$ if

$$o(c_1,\cdots ,c_n)\in C\forall c_1,\cdots ,c_n\in C$$