It can be expressed as an alternate sum of Betti numbers, and Descartes theorem equates it to the number of circles in the total defect.
For a partially ordered set, it is equal to the Mobius function of the smallest and largest elements in the set. It can be expressed as an alternate sum of Betti numbers, and Descartes theorem equates it to the number of circles in the total defect. For a two-dimensional Riemannian manifold, it is equal to the integral of the curvature divided by two pi, a result known as the Gauss-Bonnet theorem. For surfaces homeomorphic to a sphere, it is equal to 2, which is used to prove one of its namesakes' formulas. FTP, name this topological invariant often symbolized chi, that for a polyhedron is given by the number of vertices minus the number of edges plus the number of faces, a certain characteristic named for a Swiss mathematician.
For a partially ordered set, it is equal to the Mobius function of the smallest and largest elements in the set.
{Euler} characteristic