\begin{definition}[Definition:Closure (Abstract Algebra)/Algebraic Structure]
Let $\struct {S, \circ}$ be an algebraic structure.
Then $S$ has the property of '''closure under $\circ$''' {{iff}}:
:$\forall \tuple {x, y} \in S \times S: x \circ y \in S$
$S$ is said to be '''closed under $\circ$''', or just that '''$\struct {S, \circ}$ is closed'''.
\end{definition}