  Nothing so far has been said about how specifically the  “Tangent Space”  \(\Sigma(M_{p})\) is connected to the manifold.  Since \(\Sigma(M_{p})\) is supposed to be a  generalization of the ordinary tangent space which arises  intrinsically from the local differential structure of \(M\), Weyl suggests that certain embedding conditions have to be imposed on the  normal coordinates \(\xi\) of the Klein space  \(\Sigma(M_{p})\). 