Intersecting families of convex cover order m

Let S=cl(int S) be a subset of the plane, Q the set of points of local non-convexity of S, Qfinite, with p a point in (bdry S ker S) Q. If denotes the collection of allmaximal families of wedges of S having convex cover order m, m1, then the members of are characterized in the following manner: For W _o a wedge of S, W _o is in if and only if for every w _o in W _o and every collection of points w ₁, ...w _m in S, then w _i, w_j] S for at least one pair i, j, 0i<jm.AMS(MOS) Subject Classification 1970: Primary 52A10, 52A40.