The link between critical points and topology already appears at a lower level of abstraction. For example, let formula_32 be a sub-manifold of formula_33 and be a point outside formula_34 The square of the distance to of a point of formula_32 is a differential map such that each connected component of formula_32 contains at least a critical point, where the distance is minimal. It follows that the number of connected components of formula_32 is bounded above by the number of critical points.