  The special and general, as well as the non-relativistic spacetime  theories postulate various structural constraints which events are  held to satisfy. When interpreted physically, these mathematical  structures or constraints correspond to physical structural fields  (Strukturfelder). Analogous to the electromagnetic field,  these structural fields act on matter and are, within the context of  the general theory of relativity, in turn acted on by matter. An  \(n\)-dimensional manifold \(M\) whose sole properties are  those that fall under the concept of a manifold, Weyl (1918b)  physically interprets as an \(n\)-dimensional empty world, that  is, a world empty of both matter and fields. On the other hand, an  \(n\)-dimensional manifold \(M\) that is an affinely connected  manifold, Weyl physically interprets as an \(n\)-dimensional world filled with a gravitational field, and an \(n\)-dimensional  manifold \(M\) endowed with a projective structure represents an  \(n\)-dimensional non-empty world filled with an  inertial-gravitational field, or what Weyl calls the guiding  field Führungsfeld). In a  similar vein, an \(n\)-dimensional manifold \(M\) that  possesses a conformal structure of Lorentz type, represents a  non-empty \(n\)-dimensional world filled with a causal field.  Finally, an \(n\)-dimensional manifold \(M\) endowed with a  metrical structure may be interpreted physically as an  \(n\)-dimensional non-empty world filled with a metric field. 