  A boundary for a Banach space is a subset of the dual unit sphere with the
property that each element of the Banach space attains its norm on an element
of that subset. Trivially, the pointwise convergence with respect to such a
boundary is coarser than the weak topology on the Banach space. Godefroy's
Boundary Problem asks whether nevertheless both topologies have the same
bounded compact sets. This paper contains the answer in the positive.
