| Title:
|
Generalized analytic spaces, completeness and fragmentability (English) |
| Author:
|
Holický, Petr |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
51 |
| Issue:
|
4 |
| Year:
|
2001 |
| Pages:
|
791-818 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Classical analytic spaces can be characterized as projections of Polish spaces. We prove analogous results for three classes of generalized analytic spaces that were introduced by Z. Frolík, D. Fremlin and R. Hansell. We use the technique of complete sequences of covers. We explain also some relations of analyticity to certain fragmentability properties of topological spaces endowed with an additional metric. (English) |
| Keyword:
|
scattered-$K$-analytic space |
| Keyword:
|
isolated-$K$-analytic space |
| Keyword:
|
Čech analytic space |
| Keyword:
|
$\sigma $-fragmented space |
| Keyword:
|
complete sequence of covers |
| MSC:
|
54C35 |
| MSC:
|
54D15 |
| MSC:
|
54F65 |
| MSC:
|
54H05 |
| idZBL:
|
Zbl 0995.54035 |
| idMR:
|
MR1864043 |
| . |
| Date available:
|
2009-09-24T10:47:21Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127687 |
| . |
| Reference:
|
[1] Z. Frolík: Distinguished subclasses of Čech-analytic spaces (research announcement).Comment. Math. Univ. Carolin. 25 (1984), 368–370. |
| Reference:
|
[2] Z. Frolík: Generalizations of the $G_\delta $-property of complete metric spaces.Czechoslovak Math. J. 10 (85) (1960), 359–379. MR 0116305 |
| Reference:
|
[3] Z. Frolík: A survey of separable descriptive theory of sets and spaces.Czechoslovak Math. J. 20 (1970), 406–467. MR 0266757 |
| Reference:
|
[4] Z. Frolík: Čech-analytic spaces (research announcement).Comment. Math. Univ. Carolin. 25 (1984), 367–368. |
| Reference:
|
[5] R. W. Hansell: Descriptive Topology.Recent Progress in Recent Topology, North-Holland, Amsterdam, London, New York, Tokyo, 1992, pp. 275–315. Zbl 0805.54036, MR 1229129 |
| Reference:
|
[6] R. W. Hansell: Descriptive sets and the topology of nonseparable Banach spaces.Serdica Math. J. 27 (2001), 1–66. Zbl 0982.46012, MR 1828793 |
| Reference:
|
[7] R. W. Hansell: Compact perfect sets in weak analytic spaces.Topology Appl. 41 (1991), 65–72. Zbl 0759.54016, MR 1129699, 10.1016/0166-8641(91)90101-Q |
| Reference:
|
[8] P. Holický: Čech analytic and almost $K$-descriptive spaces.Czechoslovak Math. J. 43 (1993), 451–466. MR 1249614 |
| Reference:
|
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| Reference:
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[10] P. Holický: Luzin theorems for scattered-$K$-analytic spaces and Borel measures on them.Atti Sem. Mat. Fis. Univ. Modena XLIV (1996), 395–413. MR 1428772 |
| Reference:
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[11] J. E. Jayne, I. Namioka and C. A. Rogers: Topological properties of Banach spaces.Proc. London Math. Soc. 66 (1993), 651–672. MR 1207552 |
| Reference:
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[12] J. E. Jayne, I. Namioka and C. A. Rogers: Properties like the Radon-Nikodým property. Preprint.(1989). |
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| Reference:
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[14] I. Namioka: Separate continuity and joint continuity.Pacific J. Math. 51 (1974), 515–531. Zbl 0294.54010, MR 0370466, 10.2140/pjm.1974.51.515 |
| Reference:
|
[15] I. Namioka and R. Pol: $\sigma $-fragmentability and analyticity.Mathematika 43 (1996), 172–181. MR 1401716, 10.1112/S0025579300011670 |
| Reference:
|
[16] I. Namioka and R. Pol: $\sigma $-fragmentability of mappings into $C_p(K)$.Topology Appl. 89 (1998), 249–263. MR 1645164, 10.1016/S0166-8641(97)00217-4 |
| . |
