| Title:
|
On a theorem of Holický and Zelený concerning Borel maps without $\sigma$-compact fibers (English) |
| Author:
|
Milewski, P. |
| Author:
|
Pol, R. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
53 |
| Issue:
|
3 |
| Year:
|
2003 |
| Pages:
|
535-543 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper is concerned with a recent very interesting theorem obtained by Holický and Zelený. We provide an alternative proof avoiding games used by Holický and Zelený and give some generalizations to the case of set-valued mappings. (English) |
| Keyword:
|
Borel maps |
| Keyword:
|
$\sigma $-compact sections |
| Keyword:
|
set-valued maps |
| MSC:
|
26A21 |
| MSC:
|
28A05 |
| MSC:
|
54C10 |
| MSC:
|
54H05 |
| idZBL:
|
Zbl 1080.54511 |
| idMR:
|
MR2000051 |
| . |
| Date available:
|
2009-09-24T11:04:13Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127821 |
| . |
| Reference:
|
[1] J. Chaber and R. Pol: Remarks on closed relations and a theorem of Hurewicz.Topology Proc. 22 (1997), 81–94. MR 1657906 |
| Reference:
|
[2] C. Dellacherie: Un cours sur les ensembles analytiques.In: Analytic Sets, C. A. Rogers et al. (eds.), Academic Press, London, 1980, pp. 183–316. |
| Reference:
|
[3] R. Engelking: General Topology.PWN, Warszawa, 1977. Zbl 0373.54002, MR 0500780 |
| Reference:
|
[4] J. Hoffman-Jørgensen and F. Topsøe: Analytic spaces and their Application.In: Analytic Sets, C. A. Rogers et al. (eds.), Academic Press, London, 1980, pp. 317–401. |
| Reference:
|
[5] P. Holický and M. Zelený: A converse of Arsenin-Kunugui theorem on Borel sets with $\sigma $-compact sections.Fund. Math. 165 (2000), 191–202. MR 1805424 |
| Reference:
|
[6] A. S. Kechris: Classical Descriptive Set Theory.Springer-Verlag, New York, 1994. MR 1321597 |
| Reference:
|
[7] A. S. Kechris, A. Louveau and W. H. Woodin: The structure of $\sigma $-ideals of compact sets.Trans. Amer. Math. Soc. 301 (1987), 263–288. MR 0879573 |
| Reference:
|
[8] K. Kuratowski: Topology I and II.Academic Press, Warszawa, 1966 and 1968. MR 0217751 |
| Reference:
|
[9] H. Michalewski and R. Pol: On a Hurewicz-type theorem and a selection theorem of Michael.Bull. Polish Acad. Sci. Math. 43 (1995), 273–275. MR 1414783 |
| Reference:
|
[10] R. Pol: Some remarks about measurable parametrizations.Proc. Amer. Math. Soc. 93 (1985), 628–632. Zbl 0609.28006, MR 0776192, 10.1090/S0002-9939-1985-0776192-3 |
| . |
