"Geometric Properties" of Sets of Lines

Abstract

(Also cross-referenced as CAR-TR-724) When we regard the plane as a set of points, we can define various

geometric properties of subsets of the plane connectedness, convexity, area, diameter, etc. It is well known that the plane can also be regarded as a set of lines. This note considers methods of defining sets (or fuzzy sets) of lines in the plane, and of defining (analogs of) "geometric properties" for such sets.