Abstract
In this paper we give some topological characterizations of bounded Baire-I functions using some ranks. Kechris and Louveau classified the Baire-I functions to the subclasses B1(K) for every ( w. The second basic result of the paper involves the introduction of a new ordinal-rank on sequences (fr), called the 6-rank, which is smaller than the convergence rank -y. This result yields the following characterization of B? (K) : f E B4 (K) if there exists a sequence (fn) of continuous functions with fn -* f pointwise and 3((fn)) .
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