\begin{definition}[Definition:Ordered Set of Closure Systems]
Let $L$ be an ordered set.
The '''ordered set of closure systems''' of $L$ is a relational structure
:$\operatorname{ClSystems}\left({L}\right) = \left({X, \precsim}\right)$
where
:$X$ is the set of all closure systems of $L$,
:dor all closure systems $S_1 = \left({T_1, \preceq_1}\right), S_2 = \left({T_2, \preceq_2}\right)$ of $L$: $S_1 \precsim S_2 \iff T_1 \subseteq T_2$
\end{definition}