  To emphasize, the Law of Inertia and the Law of Motion, as formulated above, apply to all, relativistic or non-relativistic,  curved or flat, dynamic or non-dynamic, spacetime theories. The  reason for the general character of these laws consists in the fact  that they require for their formulation only the local differential  topological structure of spacetime, a structure which is common to  all spacetime theories. In addition, as was noted earlier in  §4.2, the affine and projective spacetime structures are  G-structures. Consequently, they may be flat or non-flat; but  they can never vanish. In theories prior to the advent of  general relativity, the affine and projective structures were flat.  It was common practice, however, to use coordinate systems that were adapted to these flat G-structures. And since in such  adapted coordinate systems the components of the affine and  projective structures vanish, it was difficult to recognize and to  appreciate the existence of these structures, and their important role in providing a coherent account of motion. 