This paper studies the essential elements (Puppe, 1996) associated with binary relations over opportunity sets. We restrict attention to binary relations which are reflexive and transitive (pre-orders) and which further satisfy a monotonicity and desirability condition. These are called opportunity relations (ORs). Our main results axiomatically characterise two important classes of ORs: those ...

In the current problem set we are investigating two problems in computational geometry using concepts from our study of the computable real numbers and calculus. The main problem we are examining is the notion of a set of points in the plane and how to compute their convex hull. In the last lecture we briefly discussed how it is possible to investigate computational geometry in a more abstract ...

A pseudo-triangle is a simple polygon with three convex vertices, and a pseudo-triangulation is a tiling of a planar region into pseudo-triangles. Pseudo-triangulations appear as data structures in computational geometry, as planar bar-and-joint frameworks in rigidity theory and as projections of locally convex surfaces. This survey of current literature includes combinatorial properties and co...