Closure

A set $S$ is closed under an operation $f$ if, whenever $f$ is fed elements of $S$, it produces another element of $S$. For example, if $f$ is a trinary operation (i.e., a function of three arguments) then "$S$ is closed under $f$" means "if $x, y, z \in S$ then $f(x, y, z) \in S$".

For example, the set [integer $\mathbb Z$] is closed under addition (because adding two integers yields another integer), but the set $\mathbb Z_5 = \{0, 1, 2, 3, 4, 5\}$ is not (because $1 + 5$ is not in $\mathbb Z_5$).