Closure Spaces in the Plane

When closure operators are deened over gures in the plane, they are normally deened with respect to convex closure in the Euclidean plane. This report concentrates on discrete closure operators deened over the discrete, rectilinear plane. Basic to geometric convexity is the concept of a geodesic, or shortest path. Such geodesics can be regarded as the closure of two points. But, given the usual deenition of geodesic in the discrete plane, they are not unique. And therefore convex closure is not uniquely generated. We ooer a diierent deenition of geodesic that is uniquely generated, although not symmetric. It results in a diierent geometry; for example, two unbounded lines may be parallel to a third, yet still themselves intersect. It is a discrete geometry that appears to be relevant to VLSI design.