"Geometric properties" of sets of lines

Abstract 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.