  Using the topological flux insertion procedure, the ground-state degeneracy
of an insulator on a periodic lattice with filling factor $\nu=p/q$ was found
to be at least $q$-fold. Applying the same argument in a lattice with edges, we
show that the degeneracy is modified by the additional edge density
$\nu_{\mysw{E}}$ associated with the open boundaries. In particular, we
demonstrate that these edge corrections may even make an insulator with integer
bulk filling degenerate.
