BF topological theories and infinitely reducible systems

We present a rigorous discussion for abelian BF theories in which the base manifold of the U(1) bundle is homeomorphic to a Hilbert space. The theory has an infinite number of stages of reducibility. We specify conditions on the base manifold under which the covariant quantization of the system can be performed unambiguously. Applications of the formulation to the superparticle and the supertstring are also discussed.