Definition:Closure of Set under Closure Operator

Definition
Let $S$ be a set.

Let $\operatorname{cl}$ be a closure operator on $S$.

Let $T \subseteq S$ be a subset of $S$.

The closure of $T$ is its image $\operatorname{cl}(T)$.

Also see

 * Definition:Closed Set under Closure Operator
 * Closure is Smallest Closed Successor