  We discuss the effect of dissipation on quantum phase transitions. In
particular we concentrate on the Superconductor to Insulator and Quantum-Hall
to Insulator transitions. By invoking a phenomenological parameter $\alpha$ to
describe the coupling of the system to a continuum of degrees of freedom
representing the dissipative bath, we obtain new phase diagrams for the quantum
Hall and superconductor-insulator problems. Our main result is that, in
two-dimensions, the metallic phases observed in finite magnetic fields
(possibly also strictly zero field) are adiabatically deformable from one to
the other. This is plausible, as there is no broken symmetry which
differentiates them.
