Point-Set Topological Spatial Relations

Practical needs in the realm of Geographic Information Systems (GISs) have driven the efforts to investigate formal and sound methods to describe spatial relations. After an introduction of the basic ideas and notions of topology, a novel theory of topological spatial relations between sets is developed in which the relations are defined in terms of the intersections of the boundaries and interiors of two sets. By considering and as the values of the intersections, a total of sixteen topological spatial relations are described, each of which can be realized in IR . This set is reduced to nine relations if the sets are restricted to spatial regions, a fairly broad class of subsets of a connected topological space having application to GIS. It is shown that these relations correspond to some of the standard set-theoretic and topological spatial relations between sets such as equality, disjointness, and containment in the interior.