The path topology and the causal completion

Abstract

It is shown that the path topology of Hawking, King, and McCarthy can be extended to the causal completion of a globally hyperbolic Lorentzian manifold. The suggested topology T is defined only in terms of chronological structures and T is finer than the extended Alexandrov topology. It is also shown that a T-homeomorphism induces a conformal isomorphism and a homeomorphism in the extended Alexandrov topology.