A term applied to a set S on whose elements a dyadic operation ° is defined and that possesses the property that, for every (s,t) in S, the quantity s ° t is also in S; S is then said to be closed under °. A similar definition holds for monadic operations such as ∼. A set S is closed under ∼ provided that, when s is in S, the quantity ∼ s is also in S.

The set of integers is closed under the usual arithmetic operations of addition, subtraction, and multiplication, but is not closed under division.