Abstract

In the present paper it is shown how it is possible by means of a time-based concept of equidistance to construct a spatial geometry for relativistic cosmology. In analogy to a sphere defined as the geometrical site for all those points which are equidistant from a given point, we construct a plane as the site for all those points that are equidistant from two points, and a line as the site for all those points equidistant from three points. Having defined parallellity and perpendicularity, we proceed to define the Cosmic Substrate in a way analogous to the cosmological principle of the Cusan. Assuming that we can always construe the center point for any three non-collinear members of this Substrate, we can prove simultaneity to be universally transitive for all members of the Substrate if the simultaneity is defined indirectly by means of equidistance.