| Title:
|
Classifications and characterizations of Baire-1 functions (English) |
| Author:
|
Kiriakouli, P. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
39 |
| Issue:
|
4 |
| Year:
|
1998 |
| Pages:
|
733-748 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $\Cal B_{1}^{\xi }(K)$, $1 \leq \xi < \omega_{1}$. (English) |
| Keyword:
|
Baire-1 functions |
| Keyword:
|
convergence index |
| Keyword:
|
oscillation index |
| Keyword:
|
trees |
| MSC:
|
46E99 |
| MSC:
|
54C30 |
| MSC:
|
54C35 |
| MSC:
|
54C50 |
| idZBL:
|
Zbl 1060.54506 |
| idMR:
|
MR1715462 |
| . |
| Date available:
|
2009-01-08T18:48:02Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119048 |
| . |
| Reference:
|
[1] Alspach D., Argyros S.: Complexity of weakly null sequences.Dissertationes Math. CCCXXI (1992), 1-44. Zbl 0787.46009, MR 1191024 |
| Reference:
|
[2] Alspach D., Odell E.: Averaging null sequences.Lectures Notes in Math. 1332, Springer, Berlin, 1988. MR 0967092 |
| Reference:
|
[3] Bourgain J.: On convergent sequences of continuous functions.Bull. Soc. Math. Belg. Ser. B 32 (1980), 235-249. Zbl 0474.54008, MR 0682645 |
| Reference:
|
[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. Zbl 0762.46006 |
| Reference:
|
[5] Kechris A.S., Louveau A.: A classification of Baire class 1 functions.Trans. Amer. Math. Soc. 318 (1990), 209-236. Zbl 0692.03031, MR 0946424 |
| Reference:
|
[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. |
| Reference:
|
[7] Kiriakouli P.: A classification of Baire-1 functions.Trans. Amer. Math. Soc., to appear. Zbl 0926.03056, MR 1407705 |
| Reference:
|
[8] Kiriakouli P.: On pointwise convergent sequences of continuous functions with continuous limits.preprint. |
| Reference:
|
[9] Kiriakouli P., Papanastassiou N.: Convergence for sequences of functions and an Egorov type theorem.preprint. Zbl 1034.28001, MR 2018591 |
| Reference:
|
[10] Mercourakis S.: On Cesaro summable sequences of continuous functions.Mathematika 42 (1995), 87-104. Zbl 0826.46001, MR 1346674 |
| Reference:
|
[11] Mercourakis S.: On some generalizations of the classical Banach-Saks properties.preprint, 1994. |
| Reference:
|
[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. Zbl 0832.46005 |
| . |
