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 $\Cal B_{1}^{\xi }(K)$, $1 \leq \xi < \omega_{1}$.
@article{119048,
author = {Persephone Kiriakouli},
title = {Classifications and characterizations of Baire-1 functions},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {39},
year = {1998},
pages = {733-748},
zbl = {1060.54506},
mrnumber = {1715462},
language = {en},
url = {http://dml.mathdoc.fr/item/119048}
}
Kiriakouli, Persephone. Classifications and characterizations of Baire-1 functions. Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) pp. 733-748. http://gdmltest.u-ga.fr/item/119048/
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