Join-closed and meet-closed subsets in complete lattices
František Machala; Vladimír Slezák
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2004)
- Volume: 43, Issue: 1, page 113-117
- ISSN: 0231-9721
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topMachala, František, and Slezák, Vladimír. "Join-closed and meet-closed subsets in complete lattices." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 43.1 (2004): 113-117. <http://eudml.org/doc/32350>.
@article{Machala2004,
abstract = {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.},
author = {Machala, František, Slezák, Vladimír},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {complete lattices; join-closed and meet-closed sets; complete lattice; join-closed set; meet-closed set},
language = {eng},
number = {1},
pages = {113-117},
publisher = {Palacký University Olomouc},
title = {Join-closed and meet-closed subsets in complete lattices},
url = {http://eudml.org/doc/32350},
volume = {43},
year = {2004},
}
TY - JOUR
AU - Machala, František
AU - Slezák, Vladimír
TI - Join-closed and meet-closed subsets in complete lattices
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2004
PB - Palacký University Olomouc
VL - 43
IS - 1
SP - 113
EP - 117
AB - 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.
LA - eng
KW - complete lattices; join-closed and meet-closed sets; complete lattice; join-closed set; meet-closed set
UR - http://eudml.org/doc/32350
ER -
References
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- Machala F., Join-independent and meet-independent sets in complete lattices, Order 18 (2001), 269–274. Zbl1009.06005MR1867237
- Machala F., Slezák V., Lattice-inadmissible incidence structures, Discuss. Math. (submitted). Zbl1073.06004
- Slezák V., On the special context of independent sets, Discuss. Math., Gen. Algebra and Appl. 21 (2001), 115–122. Zbl0997.06003MR1868622
- Szász G.: Introduction to Lattice Theory., Akadémiai Kiadó, , Budapest, 1963. (1963) MR0166118
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