  We study bosonization ambiguities in two dimensional quantum electrodynamics
in the presence and in the absence of topologically charged gauge fields. The
computation of fermionic correlation functions suggests that ambiguities may be
absent in nontrivial topologies, provided that we do not allow changes of
sector as we evaluate functional integrals. This would remove an infinite
arbitrariness from the theory. In the case of trivial topologies, we find upper
and lower bounds for the Jackiw-Rajaraman parameter, corresponding to the
limiting cases of regularizations which preserve gauge or chiral symmetry.
