  We discuss the topological nature of the boundary spacetime, the conformal
infinity of the ambient cosmological metric. Due to the existence of a
homothetic group, the bounding spacetime must be equipped not with the usual
Euclidean metric topology but with the Zeeman fine topology. This then places
severe constraints to the convergence of a sequence of causal curves and the
extraction of a limit curve, and also to our ability to formulate conditions
for singularity formation.
