Abstract:Kechris and Louveau in [5] classified the bounded Baire-1 functions, which are defined on a compact metric space $K$, to the subclasses ${\Cal B}_{1}^{\xi }(K)$, $\xi < \omega _1$. In [8], for every ordinal $\xi < \omega _{1}$ we define a new type of convergence for sequences of real-valued functions ($\xi $-uniformly pointwise) which is between uniform and pointwise convergence. In this paper using this type of convergence we obtain a classification of pointwise convergent sequences of continuous real-valued functions defined on a compact metric space $K$, and also we give a characterization of the classes ${\Cal B}_{1}^{\xi }(K)$, $1 \leq \xi < \omega _{1}$.
Keywords: Baire-1 functions, convergence index, oscillation index, trees
AMS Subject Classification: 46E99, 54C30, 54C35, 54C50