In mathematics, a closure operator on a set S is a function cl : P → P {\displaystyle \operatorname {cl} :{\mathcal {P}}\rightarrow {\mathcal {P}}} from the power set of S to itself that satisfies the following conditions for all sets X, Y ⊆ S {\displaystyle X,Y\subseteq S} Closure operators are determined by their closed sets, i.e., by the sets of the form cl, since the closure cl of a set X is the smallest closed set containing X. Such families of "closed sets" are sometimes called closure systems or "Moore families". Wikipedia