Definition:Closure (Abstract Algebra)

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

$$S$$ is defined as being closed under $$\circ$$, or $$\left({S, \circ}\right)$$ is closed iff:

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

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