Geometric containment orders: A survey (Q1300338)

A partially ordered set \((P,<)\) is called a geometric containment order of some type if there is a mapping from \(P\) into the set of objects of a given type in a finite-dimensional Euclidean space that preserves \(<\) by proper inclusion. The paper is a survey on results about geometric containment orders related mainly to angular regions. convex polygons and circles in the plane, and spheres of all dimensions. Further problems concerning the subject (e.g. relations to incidence orders in graphs, hypergraphs, etc.) are also discussed.