Posets via partial closure operators. (English) Zbl 0965.06003

Dorninger, D. (ed.) et al., Contributions to general algebra 12. Proceedings of the 58th workshop on general algebra “58. Arbeitstagung Allgemeine Algebra”, Vienna, Austria, June 3-6, 1999. Klagenfurt: Verlag Johannes Heyn. 371-375 (2000).
The authors introduce partial closure operators and partial closure systems on sets, describe connections between them, and show that every partially ordered set is isomorphic to a partial closure system ordered by set-inclusion. Further, they define complete partial closure operators and complete partial closure systems, and find their relations to complete partially ordered sets. In addition, analogous connections are obtained for algebraic partial closure systems, operators and partially ordered sets.
For the entire collection see [Zbl 0942.00022].


06A06 Partial orders, general
06A15 Galois correspondences, closure operators (in relation to ordered sets)