  Seiberg and Witten have discussed a specifically "stringy" kind of
instability which arises in connection with "large" branes in asymptotically
AdS spacetimes. It is easy to see that this instability actually arises in most
five-dimensional asymptotically AdS black hole string spacetimes with
non-trivial horizon topologies. We point out that this is a more serious
problem than it may at first seem, for it cannot be resolved even by taking
into account the effect of the branes on the geometry of spacetime. [It is
ultimately due to the {\em topology} of spacetime, not its geometry.] Next,
assuming the validity of some kind of dS/CFT correspondence, we argue that
asymptotically deSitter versions of the Hull-Strominger-Gutperle S-brane
spacetimes are also unstable in this "topological" sense, at least in the case
where the R-symmetries are preserved. We conjecture that this is due to the
unrestrained creation of "late" branes, the spacelike analogue of large branes,
at very late cosmological times.
