Characterizations of the Generalized Convex Kernel
Arthur G. Sparks · Proceedings of the American Mathematical Society · 1971
It is well known that the convex kernel $K$ of a set $S$ is the intersection of all maximal convex subsets of $S$. In this paper it is shown that the $n$th order kernel of a compact, simply-connected set $S$ in the plane is an ${L_n}$ set and is, in fact, the intersection of all maximal ${L_n}$ subsets of $S$. Furthermore, it is shown that one does not have to intersect the family of all the maximal ${L_n}$ subsets to obtain the $n$th order kernel, but that any subfamily thereof which covers the set is sufficient.