On the special context of independent sets

Vladimír Slezák

Discussiones Mathematicae - General Algebra and Applications (2001)

  • Volume: 21, Issue: 1, page 115-122
  • ISSN: 1509-9415

Abstract

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In this paper the context of independent sets is assigned to the complete lattice (P(M),⊆) of all subsets of a non-empty set M. Some properties of this context, especially the irreducibility and the span, are investigated.

How to cite

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Vladimír Slezák. "On the special context of independent sets." Discussiones Mathematicae - General Algebra and Applications 21.1 (2001): 115-122. <http://eudml.org/doc/287693>.

@article{VladimírSlezák2001,
abstract = {In this paper the context of independent sets $J^\{p\}_\{L\}$ is assigned to the complete lattice (P(M),⊆) of all subsets of a non-empty set M. Some properties of this context, especially the irreducibility and the span, are investigated.},
author = {Vladimír Slezák},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {context; complete lattice; join-independent and meet-independent sets; join-independent; meet-independent; distances; irreducibility; spans; contexts},
language = {eng},
number = {1},
pages = {115-122},
title = {On the special context of independent sets},
url = {http://eudml.org/doc/287693},
volume = {21},
year = {2001},
}

TY - JOUR
AU - Vladimír Slezák
TI - On the special context of independent sets
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2001
VL - 21
IS - 1
SP - 115
EP - 122
AB - In this paper the context of independent sets $J^{p}_{L}$ is assigned to the complete lattice (P(M),⊆) of all subsets of a non-empty set M. Some properties of this context, especially the irreducibility and the span, are investigated.
LA - eng
KW - context; complete lattice; join-independent and meet-independent sets; join-independent; meet-independent; distances; irreducibility; spans; contexts
UR - http://eudml.org/doc/287693
ER -

References

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  1. [1] V. Dlab, Lattice formulation of general algebraic dependence, Czechoslovak Math. Journal 20 (1970), 603-615. Zbl0247.06006
  2. [2] B. Ganter, R. Wille, Formale Begriffsanalyse - Mathematische Grundlagen, Springer-Verlag, Berlin 1996. (English version: 1999). 
  3. [3] K. Głazek, Some old and new problems in the independence theory, Colloq. Math. 42 (1979), 127-189. Zbl0432.08001
  4. [4] G. Gratzer, General Lattice Theory, Birkhäuser-Verlag, Basel 1998. Zbl0909.06002
  5. [5] F. Machala, Incidence structures of independent sets, Acta Univ. Palacki Olomuc., Fac. Rerum Natur., Math. 38 (1999), 113-118. Zbl0974.08001
  6. [6] F. Machala, Join-independent and meet-independent sets in complete lattices, Order (submitted). Zbl1009.06005
  7. [7] E. Marczewski, Concerning the independence in lattices, Colloq. Math. 10 (1963), 21-23. Zbl0122.25802
  8. [8] V. Slezák, Span in incidence structures defined on projective spaces, Acta Univ. Palack. Olomuc., Fac. Rerum Natur., Mathematica 39 (2000), 191-202. Zbl1039.08001
  9. [9] G. Szász, Introduction to Lattice Theory, Akadémiai Kiadó, Budapest 1963. 
  10. [10] G. Szász, Marczewski independence in lattices and semilattices, Colloq. Math. 10 (1963), 15-20. Zbl0118.02401

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