Causal boundaries for general relativistic space--times

Let M be a causally continuous space-time. Using indecomposable past and future sets in a symmetric way we construct a causal completion N for M. N is a causal space; the chronology of M in N is the chronology of M. The extended Alexandrov topology for N makes N Hausdorff and M a densely imbedded subspace. M is globally hyperbolic iff either the chronological future or the chronological past of each point in N-M is empty, causally simple iff the causality of M in N is the causality of M. The standard examples of causal completions are special cases.