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Join-closed and meet-closed subsets in complete lattices

František Machala, Vladimír Slezák (2004)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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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