  In Weyl (1929e, 1988) and to a lesser extent in Weyl (1938a), Weyl objected to Cartan’s approach by noting that Cartan’s “Tangent Space”, namely the Klein space \(\Sigma(M_{p})\) associated with each point of the manifold \(M\), does not arise intrinsically from the differential structure of the manifold the way the ordinary tangent vector space does. Weyl therefore noted that it is necessary to impose certain non-intrinsic embedding conditions on \(\Sigma(M_{p})\) that specify how the “Tangent Space” \(\Sigma(M_{p})\) is associated with each point of the manifold \(M\). Paraphrasing Weyl, the situation is as follows: We assume that we can associate a copy \(\Sigma(M_{p})\) of a given Klein space with each point \(p\) of the manifold \(M\) and that the displacement of the Klein space \(\Sigma(M_{p})\) at \(p \in M\) to the Klein space \(\Sigma(M_{p'})\) associated with an infinitely nearby point \(p'\in M\), constitutes an isomorphic representation of \(\Sigma(M_{p})\) on \(\Sigma(M_{p'})\) by means of an infinitesimal action of the group \(G\). In choosing an admissible frame of reference \(f\) for each Klein space \(\Sigma(M_{p})\), their points are represented by normal coordinates \(\xi\). Any two frames  \(f,f'\) are related by a group  element \(s \in G\), and a succession of transformations \(f \rightarrow f'\) and \(f' \rightarrow f''\) by \(s \in G\) and  \(t \in G\) respectively, relates \(f\) and  \(f''\) by the group composition \(t \circ s \in G\). 