Definition:Closed Element/Definition 2

Definition
Let $\struct {S, \preceq}$ be an ordered set.

Let $\cl$ be a closure operator on $S$.

Let $x \in S$.

The element $x$ is a closed element of $S$ (with respect to $\cl$) $x$ is in the image of $\cl$:
 * $x \in \Img \cl$

Also see

 * Equivalence of Definitions of Closed Element