Abstract
There are well-known isomorphisms between the complete lattice of all partitions of a given set A and the lattice of all equivalence relations on A. In the paper the notion of partition is generalized in order to work correctly for wider classes of binary relations than equivalence ones such as quasiorders or tolerance relations. Some others classes of binary relations and corresponding counterparts of partitions are considered.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Bandelt H. J.: Tolerance relations on lattices. Bulletin of the Australian Mathematical Society 23, 367–381 (1981)
Chajda I., Niederle J., B. Zelinka: On existence conditions for compatible tolerances. Czechoslovak Mathematical Journal 26, 304–315 (1976)
Chajda I., Zelinka B.: Tolerance relation on lattices. Casopis pro pestováni matematiky 99, 394–399 (1974)
Chajda I., Zelinka B.: Minimal compatible tolerances on lattices. Czechoslovak Mathematical Journal 27, 452–459 (1977)
Czédli G.: Factor lattices by tolerances. Acta Scientiarum Mathematicarum, Szeged. 44, 35–42 (1982)
Day A., Herrmann Ch.: Gluings of modular lattices. Order. 5, 85–101 (1988)
Denecke K., Erné M., Wismath S. L. (eds.), Galois Connections and Applications. Kluwer, Dordrecht (2004)
Domenach F., Domenach F.: Biclosed binary relations and Galois connections. Order. 18, 89–104 (2001)
Grygiel, J., The Concept of Gluing for Lattices, Wydawnictwo WSP Czȩstochowa, Poland, 2004.
Zeeman, E. C., The topology of the brain and visual perception, in M. K. Fort (ed.), The Topology of 3-Manifolds and Related Topics, Prentice-Hall, Englewood Cliffs, 1962, pp. 240–256.
Zelinka B.: Tolerances in algebraic structures.. Czechoslovak Mathematical Journal. 20, 179–183 (1970)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.
About this article
Cite this article
Nowak, M. On Some Generalizations of the Concept of Partition. Stud Logica 102, 93–116 (2014). https://doi.org/10.1007/s11225-012-9465-0
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11225-012-9465-0