Separoids, Their Categories and a Hadwiger-Type Theorem for Transversals
(Citations: 12)
In this paper we study the topology of transversals to a family of convex sets as a subset of a Grassmanian manifold. This topology seems to be ruled by a combinatorial structure which we call a separoid. With these combinatorial objects and the topological notion of virtual transversal we prove a Borsuk-Ulam-type theorem which has as a corollary a generalization of Hadwiger's theorem.