Definition:Closed Element

Definition
Let $\left({S, \preceq}\right)$ be an ordered set.

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

Let $x \in S$.

Also see

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

Special case

 * Definition:Closed Set under Closure Operator