Causal groups of space-time

The present paper is concerned with a finite dimensional space, considered as a real ordered linear space, directed with respect to a partial ordering relation (causal relation) in which a given reflexion (called temporal inversion) is antiisotone and the positive cone is closed in the euclidean topology.A generalized Zeeman theorem [1] is obtained, which states that the causal group relative to the causal relation is a subgroup of the affine group ofM.