Definition:Closed Element/Definition 1

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 a fixed point of $\cl$:
 * $\map \cl x = x$

Also see

 * Equivalence of Definitions of Closed Element