On circle containment orders
A partially ordered set is called a circle containment order provided it is isomorphic to a poset of circles in the plane ordered by inclusion. In this paper it is shown that the infinite three-dimensional poset \({\mathcal Z}^ 3\) is not a circle containment order. This fact contrasts with the conjecture that every finite three-dimensional poset is a circle order.
scientific article; zbMATH DE number 4091570