The measure for the finite union of compact convex sets that is homogenous degree zero is this property according to Hadwiger's theorem.
The measure for the finite union of compact convex sets that is homogenous degree zero is this property according to Hadwiger's theorem. As a corollary of the Poincare Duality theorem it can be shown that for a connected manifold that is the boundary of a compact manifold, this property is even. More generally, it can be defined as the alternating sum of the nth Betti number where n represents the rank of the homology group. This times 2pi equals the integral curvature of the surface that it defines. The only closed compact surfaces that have a zero value for this property are the torus and the Klein bottle. For 10 points, name this topological invariant classically defined for polyhedra as the number of vertices minus the sum of edges and faces named after a Swiss mathematician and usually denoted with the Greek letter chi.
The measure for the finite union of compact convex sets that is homogenous degree zero is this property according to Hadwiger's theorem.
{Euler characteristic} [accept {Euler number}]