BF Topological Theories and Infinitely Reducible Systems

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