Definition:Ordered Set of Closure Systems

Definition
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 $L$: $S_1 \precsim S_2 \iff T_1 \subseteq T_2$

Also See

 * Ordered Set of Closure Systems is Ordered Set