  This manuscript studies manifolds-with-boundary collapsing in the
Gromov-Hausdorff topology. The main aim is an understanding of the relationship
of the topology and geometry of a limiting sequence of manifolds-with-boundary
to that of a limit space, which is presumed to be without geodesic terminals.
  The main result establishes a disc bundle structure for any
manifold-with-boundary having two-sided bounds on sectional curvature and
second fundamental form, and a lower bound on intrinsic injectivity radius,
which is sufficiently close in the Gromov-Hausdorff topology to a closed
manifold.
  The second main result identifies Gromov-Hausdorff limits of certain
sequences of manifolds-with-boundary as Alexandrov spaces of curvature bounded
below.
