  Topology change is considered to be a necessary feature of quantum gravity by
some authors, and impossible by others. One of the main arguments against it is
that spacetimes with changing spatial topology have bad causal properties.
Borde and Sorkin proposed a way to avoid this dilemma by considering topology
changing spacetimes constructed from Morse functions, where the metric is
allowed to vanish at isolated points. They conjectured that these Morse
spacetimes are causally continuous (hence quite well behaved), as long as the
index of the Morse points is different from $1$ and $n-1$. In this paper, we
prove a special case of this conjecture. We also argue, heuristically, that the
original conjecture is actually false, and formulate a refined version of it.
