  According to Weyl, the “Tangent Space” \(\Sigma(M_{p})\) is not uniquely determined by the differential structure of \(M\). If \(G\) were the affine group, Weyl says, then the conditions above would fully specify the normal coordinate system \(\xi^{\alpha}\) on \(\Sigma(M_{p})\) as a function of the chosen local coordinates \(x^{i}\) on \(M\). Since this is not the case if \(G\) is a more extensive group than the affine group, Weyl concludes that the “Tangent Space”  \(\Sigma(M_{p})\) “is not as yet uniquely  determined by the nature of \(M\), and so long as this is not  accomplished we can not say that Cartan’s theory deals only with the  manifold \(M\).” Weyl adds: 