In models of spacetime that are the product of a four-dimensional spacetime
with an ``extra'' dimension, there is the possibility that the extra dimension
will collapse to zero size, forming a singularity. We ask whether this collapse
is likely to destroy the spacetime. We argue, by an appeal to the
four-dimensional cosmic censorship conjecture, that--at least in the case when
the extra dimension is homogeneous--such a collapse will lead to a singularity
hidden within a black string. We also construct explicit initial data for a
spacetime in which such a collapse is guaranteed to occur and show how the
formation of a naked singularity is likely avoided.Comment: Uses revtex
