Closure Operator

A closure operator on a set X is a map cl: P(X) → P(X) that assigns to each subset A its closure cl(A) and satisfies three axioms: extensivity (A ⊆ cl(A)), monotonicity (A ⊆ B ⇒ cl(A) ⊆ cl(B)), and idempotence (cl(cl(A)) = cl(A)). In topology cl(A) is the smallest closed superset of A.