  Here we prove that under a lower sectional curvature bound, a sequence of
Riemannian manifolds diffeomorphic to the standard $m$-dimensional torus cannot
converge in the Gromov--Hausdorff sense to a closed interval.
  The proof is done by contradiction by analyzing suitable covers of a
contradicting sequence, obtained from the Burago--Gromov--Perelman
generalization of the Yamaguchi fibration theorem.
