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complete lattices; join-closed and meet-closed sets
To every subset $A$ of a complete lattice $L$ we assign subsets $J(A)$, $M(A)$ and define join-closed and meet-closed sets in $L$. Some properties of such sets are proved. Join- and meet-closed sets in power-set lattices are characterized. The connections about join-independent (meet-independent) and join-closed (meet-closed) subsets are also presented in this paper.
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