\begin{definition}[Definition:Closed Element/Definition 1]
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 $\cl$)''' {{iff}} $x$ is a fixed point of $\cl$:
:$\map \cl x = x$
\end{definition}