Paper Info
Title
Contact, closure, topology, and the linking of row and column types of relations
Abstract
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 2X and that of a closure operation on 2X 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.
Year
DOI
Venue
2011
10.1016/j.jlap.2011.04.007
The Journal of Logic and Algebraic Programming
Keywords
DocType
Volume
Relation algebra,Partial order,Complete lattice,Contact relation,Closure operation,Topological structure,Open set topology,Column types,Row types,RelView
Journal
80
Issue
ISSN
Citations 
6
1567-8326
4
PageRank 
References 
Authors
0.48
8
2
Name
Order
Citations
PageRank
Gunther Schmidt120330.70
Rudolf Berghammer256976.48