  Coordinates are introduced on the Mf [manifold] in the most direct  way through the mapping onto the number space, in such a way, that  all coordinates, which arise through one-to-one continuous  transformations, are equally possible. With this the coordinate  concept breaks loose from all special constructions to which it was  bound earlier in geometry. In the language of relativity this means:  The coordinates are not measured, their values are not read off from  real measuring rods which react in a definite way to physical fields  and the metrical structure, rather they are a priori placed in the  world arbitrarily, in order to characterize those physical fields  including the metric structure numerically. The metric structure  becomes through this, so to speak, freed from space; it becomes an  existing field within the remaining structure-less space. Through  this, space as form of appearance contrasts more clearly with its  real content: The content is measured after the form is arbitrarily  related to coordinates.