  When time reversal symmetry is present there is a sharp distinction between
topological and trivial band insulators which ensures that, as parameters are
varied, these phases are separated by a phase transition at which the bulk gap
closes. Surprisingly we find that even in the absence of time reversal
symmetry, gapless regions originating from the phase boundaries persist.
Moreover the critical line generically opens up to enclose Chern insulating
phases that are thin but of finite extent in the phase diagram. We explain the
topological origin of this effect in terms of quantized charge pumping, showing
in particular that it is robust to the effect of disorder and interactions.
