  In earlier work, we analyzed the impossibility of codimension-one collapse
for surfaces of negative Euler characteristic under the condition of a lower
bound for the Gaussian curvature. Here we show that, under similar conditions,
the torus cannot collapse to a segment. Unlike the torus, the Klein bottle can
collapse to a segment; we show that in such a situation, the loops in a short
basis for homology must stay a uniform distance apart.
