  Considering the general case of \(n\) dimensions, and using Lie  groups and Lie algebras, Sophus Lie, (Lie (1886/1935, 1890a,b)),  later developed and improved Helmholtz’s justification. However, the  Helmholtz-Lie treatment of, and solution to, the problem of space,  lost its relevance with the arrival of Einstein’s theory of general  relativity. As Weyl (1922b) points out, instead of a  three-dimensional continuum we must now consider a four-dimensional  continuum, the metric of which is not positive definite but  is given instead by an indefinite quadratic form. In  addition, Helmholtz’s presupposition of metric homogeneity no longer  holds, since we are now dealing with an inhomogeneous metric field  that causally depends on the distribution of matter. Consequently,  Weyl provided a reformulation of the space problem that is compatible with the causal and metric structures postulated by the theory of  general relativity. But Weyl went further. Such a reformulation  should not only incorporate Riemann’s infinitesimal  standpoint, as required by Einstein’s general theory, it should also  cohere with Weyl’s requirements of a pure  infinitesimal geometry developed earlier in the  context of Weyl’s construction of a unified field theory. 