 In the plane, the index takes the value -1 at a saddle singularity but +1 at a source or sink singularity.Let the dimension of the manifold on which the vector field is defined be n. Take a small sphere S around the zero so that no other zeros lie in the interior of S. A map from this sphere to a unit sphere of dimensions "n" − 1 can be constructed by dividing each vector on this sphere by its length to form a unit length vector, which is a point on the unit sphere Sn-1.This defines a continuous map from S to Sn-1.