Gunther Schmidt: RATH-Paper

Authors

Title

Status, Abstract

Rudolf Berghammer
Institut für Informatik Christian-Albrechts-Universität zu Kiel
Olshausenstr. 40, 24098 Kiel, Germany
rub@informatik.uni-kiel.de
Contact, closure, topology, and the linking of row and column types of relations
.pdf .bib

Journal of Logic and Algebraic Programming 80 (6) 2011, 339-361

Extended version

Gunther Schmidt

Fakultät für Informatik
Universität der Bundeswehr München
85577 Neubiberg, Germany
Gunther.Schmidt@UniBw.de
2011 Forming closures of subsets of a set X is a technique that plays an important role in many scientific disciplines and there are many cryptomorphic mathematical structures that describe closures and their construction. One of them was introduced by Aumann in the year 1970 under the name contact relation. Using relation algebra, we generalize Aumann's notion of a contact relation between X and its powerset P(X) and that of a closure operation on P(X) from powersets to general membership relations and their induced partial orders. We also investigate the relationship between contacts and closures in this general setting and present some applications. In particular, we investigate the connections between contacts, closures and topologies and use contacts to establish a one-to-one correspondence between the column intersections space and the row intersections space of arbitrary relations.

Authors		Title	Status, Abstract
Rudolf Berghammer	Institut für Informatik Christian-Albrechts-Universität zu Kiel Olshausenstr. 40, 24098 Kiel, Germany rub@informatik.uni-kiel.de	Contact, closure, topology, and the linking of row and column types of relations .pdf .bib	Journal of Logic and Algebraic Programming 80 (6) 2011, 339-361 Extended version
Gunther Schmidt	Fakultät für Informatik Universität der Bundeswehr München 85577 Neubiberg, Germany Gunther.Schmidt@UniBw.de	2011	Forming closures of subsets of a set X is a technique that plays an important role in many scientific disciplines and there are many cryptomorphic mathematical structures that describe closures and their construction. One of them was introduced by Aumann in the year 1970 under the name contact relation. Using relation algebra, we generalize Aumann's notion of a contact relation between X and its powerset P(X) and that of a closure operation on P(X) from powersets to general membership relations and their induced partial orders. We also investigate the relationship between contacts and closures in this general setting and present some applications. In particular, we investigate the connections between contacts, closures and topologies and use contacts to establish a one-to-one correspondence between the column intersections space and the row intersections space of arbitrary relations.