  We investigate how a dynamical mass of a fermion is affected by a topological
mass of a gauge field in a Maxwell-Chern-Simons $QED_3$ coupled with a
two-component fermion. The dynamical mass and also a parity condensate are
estimated by using a non-perturbative Schwinger-Dyson method. In particular, we
study a limit of vanishing the topological mass in detail and clarify a linking
between theories with and without a Chern-Simons term in a non-perturbative
level.
