Theory of ordered spaces (Q2276797)

The presented investigations of ordered sets based on some ideas and models of theoretical physics consider as a fundamental object a nonempty set M endowed with a special partial order and a distinguished family of totally ordered subsets of M - called light rays - satisfying four axioms extracted from the physical model of the space of events. Except of some structural assertions (including the polygon lemma which says that any point y of the principal end \(C_ x\) generated by x can be ``reached'' from x by traversing a finite number of light-ray segments) there is introduced a concept of D-sets (intersection sets) and regular D-sets which form a base for a Hausdorff topology. This topology coincides with the usual topology for Minkowski spaces.