Classifications and characterizations of Baire-1 functions

Persephone Kiriakouli

Commentationes Mathematicae Universitatis Carolinae (1998)

  • Volume: 39, Issue: 4, page 733-748
  • ISSN: 0010-2628

Abstract

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Kechris and Louveau in [5] classified the bounded Baire-1 functions, which are defined on a compact metric space K , to the subclasses ℬ 1 ξ ( K ) , ξ < ω 1 . In [8], for every ordinal ξ < ω 1 we define a new type of convergence for sequences of real-valued functions ( ξ -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 ℬ 1 ξ ( K ) , 1 ≤ ξ < ω 1 .

How to cite

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Kiriakouli, Persephone. "Classifications and characterizations of Baire-1 functions." Commentationes Mathematicae Universitatis Carolinae 39.4 (1998): 733-748. <http://eudml.org/doc/248248>.

@article{Kiriakouli1998,
abstract = {Kechris and Louveau in [5] classified the bounded Baire-1 functions, which are defined on a compact metric space $K$, to the subclasses $\mathcal \{B\}_\{1\}^\{\xi \}(K)$, $\xi < \omega _1$. 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 $\mathcal \{B\}_\{1\}^\{\xi \}(K)$, $1 \le \xi < \omega _\{1\}$.},
author = {Kiriakouli, Persephone},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Baire-1 functions; convergence index; oscillation index; trees; Baire-1 functions; convergence index; oscillation index; trees},
language = {eng},
number = {4},
pages = {733-748},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Classifications and characterizations of Baire-1 functions},
url = {http://eudml.org/doc/248248},
volume = {39},
year = {1998},
}

TY - JOUR
AU - Kiriakouli, Persephone
TI - Classifications and characterizations of Baire-1 functions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1998
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 39
IS - 4
SP - 733
EP - 748
AB - Kechris and Louveau in [5] classified the bounded Baire-1 functions, which are defined on a compact metric space $K$, to the subclasses $\mathcal {B}_{1}^{\xi }(K)$, $\xi < \omega _1$. 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 $\mathcal {B}_{1}^{\xi }(K)$, $1 \le \xi < \omega _{1}$.
LA - eng
KW - Baire-1 functions; convergence index; oscillation index; trees; Baire-1 functions; convergence index; oscillation index; trees
UR - http://eudml.org/doc/248248
ER -

References

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  9. Kiriakouli P., Papanastassiou N., Convergence for sequences of functions and an Egorov type theorem, preprint. Zbl1034.28001MR2018591
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