  The two--dimensional topological BF model is considered in the Landau gauge
in the framework of perturbation theory. Due to the singular behaviour of the
ghost propagator at long distances, a mass term to the ghost fields is
introduced as infrared regulator. Relying on the supersymmetric algebraic
structure of the resulting massive theory, we study the infrared and
ultraviolet renormalizability of the model, with the outcome that it is
perturbatively finite.
