Construction and properties of space-timeb-boundaries

A criterion is given for two curves of finite generalized affine length to define the same point of the b-boundary of a space-time. It is shown that the b-boundary can be constructed on every closed subbundle of the bundle of linear frames to which the Levi-Civita connection is reducible. It follows that, for any product space-time, the space-time together with its b-boundary is homeomorphic to a product of pseudo-Riemannian spaces with b-boundary. Furthermore, it is shown that maps of one space-time in to another which are isomorphisms of the connections can be C⁰-extended to the space-time with b-boundary. In particular, it follows that the group of affine transformations and the group of isometries of a space-time act as topological transformation groups on the spacetime with b-boundary.