The authors' aims in this volume are to study the subtleties of both the Cauchy boundary for any generalised (possibly non-symmetric) distance and the Gromov compactification for any (possibly incomplete) Finsler manifold; to introduce the new Busemann compactification $M_B$, relating it with the previous two completions; and to give a full description of the causal boundary $\partial V$ of any standard conformally stationary spacetime.
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