SPHERE ORDER REPRESENTATION OF POSETS AND SPACE-TIME

A space-time can be regarded as a partially ordered set by causal relations. Space-times which can be continuously represented by spheres in Euclidean space are rare. There are various definitions for dimension of a poset. In this paper, it is shown that the definition of dimension sphere ordering is equivalent to the definition of dimension Euclidian and by an example is given a technique to find the space-times that can not admit a sphere order representation