Definition:Closure (Abstract Algebra)/Algebraic Structure

Definition
Let $\left({S, \circ}\right)$ be an algebraic structure.

Then $S$ has the property of closure under $\circ$ iff:


 * $\forall \left({x, y}\right) \in S \times S: x \circ y \in S$

One says $S$ is closed under $\circ$, or $\left({S, \circ}\right)$ is closed.

Some authors use stable under $\circ$ for closed under $\circ$.