Causal boundary for strongly causal spacetimes: Pt. 1

In a previous paper an analysis of the general structure of the causal boundary constructions and a new explicit identification rule, built up from elementary TIP-TIF gluings, were presented. In the present paper we complete our identification by incorporating TIP-TIP and TIF-TIF gluings as well. An asymptotic causality condition is found which, for physically important cases, ensures the uniqueness of the endpoints of the non-spacelike curves in the completed spacetime. (author)