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. The index of the vector field at the point is the degree of this map. It can be shown that this integer does not depend on the choice of S, and therefore depends only on the vector field itself.