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