Definition:Ordered Set of Closure Systems
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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
Sources
- 1980: G. Gierz, K.H. Hofmann, K. Keimel, J.D. Lawson, M.W. Mislove and D.S. Scott: A Compendium of Continuous Lattices
- Mizar article WAYBEL10:def 3