Geodesic
Classifications and characterizations of Baire-1 functions
Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) no. 4, pp. 733-748.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 $\Cal B_{1}^{\xi }(K)$, $1 \leq \xi \omega_{1}$.
Classification : 46E99, 54C30, 54C35, 54C50
Keywords: Baire-1 functions; convergence index; oscillation index; trees 
@article{CMUC_1998__39_4_a8,
     author = {Kiriakouli, P.},
     title = {Classifications and characterizations of {Baire-1} functions},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {733--748},
     publisher = {mathdoc},
     volume = {39},
     number = {4},
     year = {1998},
     mrnumber = {1715462},
     zbl = {1060.54506},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1998__39_4_a8/}
}
TY  - JOUR
AU  - Kiriakouli, P.
TI  - Classifications and characterizations of Baire-1 functions
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 1998
SP  - 733
EP  - 748
VL  - 39
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_1998__39_4_a8/
LA  - en
ID  - CMUC_1998__39_4_a8
ER  - 
%0 Journal Article
%A Kiriakouli, P.
%T Classifications and characterizations of Baire-1 functions
%J Commentationes Mathematicae Universitatis Carolinae
%D 1998
%P 733-748
%V 39
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_1998__39_4_a8/
%G en
%F CMUC_1998__39_4_a8
Kiriakouli, P. Classifications and characterizations of Baire-1 functions. Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) no. 4, pp. 733-748. http://geodesic.mathdoc.fr/item/CMUC_1998__39_4_a8/