Geodesic
Join-closed and meet-closed subsets in complete lattices
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 43 (2004) no. 1, pp. 113-117.

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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.
Classification : 06B23, 08A02, 08A05
Keywords: complete lattices; join-closed and meet-closed sets 
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     title = {Join-closed and meet-closed subsets in complete lattices},
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Machala, František; Slezák, Vladimír. Join-closed and meet-closed subsets in complete lattices. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 43 (2004) no. 1, pp. 113-117. http://geodesic.mathdoc.fr/item/AUPO_2004__43_1_a10/