Definition:Closed Set/Closure Operator

Definition
Let $S$ be a set.

Let $\cl: \powerset S \to \powerset S$ be a closure operator.

Let $T \subseteq S$ be a subset.

Also see

 * Equivalence of Definitions of Closed Set under Closure Operator
 * Definition:Closure of Set under Closure Operator

Generalization

 * Definition:Closed Element under Closure Operator