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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  2. Alspach D., Odell E., Averaging null sequences, Lectures Notes in Math. 1332, Springer, Berlin, 1988. MR0967092
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  4. Haydon R., Odell E., Rosenthal H., On certain classes of Baire-1 functions with applications to Banach space theory, Longhorn Notes, The University of Texas at Austin, Functional Analysis Seminar 1987-89. Zbl0762.46006
  5. Kechris A.S., Louveau A., A classification of Baire class 1 functions, Trans. Amer. Math. Soc. 318 (1990), 209-236. (1990) Zbl0692.03031MR0946424
  6. Kiriakouli P., Namioka spaces, Baire-1 functions, Combinatorial principles of the type of Ramsey and their applications in Banach spaces theory (in Greek), Doctoral Dissertation, Athens Univ., 1994. 
  7. Kiriakouli P., A classification of Baire-1 functions, Trans. Amer. Math. Soc., to appear. Zbl0926.03056MR1407705
  8. Kiriakouli P., On pointwise convergent sequences of continuous functions with continuous limits, preprint. 
  9. Kiriakouli P., Papanastassiou N., Convergence for sequences of functions and an Egorov type theorem, preprint. Zbl1034.28001MR2018591
  10. Mercourakis S., On Cesaro summable sequences of continuous functions, Mathematika 42 (1995), 87-104. (1995) Zbl0826.46001MR1346674
  11. Mercourakis S., On some generalizations of the classical Banach-Saks properties, preprint, 1994. 
  12. Mercourakis S., Negrepontis S., Banach spaces and topology II, Recent Progress in General Topology, M. Hušek and J. van Mill, eds., Elsevier Science Publishers B.V., 1992, pp.495-536. Zbl0832.46005

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