Article
Full entry |
PDF
(0.5 MB)
Feedback
PDF
(0.5 MB)
Feedback
Keywords:
scattered-$K$-analytic space; isolated-$K$-analytic space; Čech analytic space; $\sigma $-fragmented space; complete sequence of covers
scattered-$K$-analytic space; isolated-$K$-analytic space; Čech analytic space; $\sigma $-fragmented space; complete sequence of covers
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.
References:
[1] Z. Frolík: Distinguished subclasses of Čech-analytic spaces (research announcement). Comment. Math. Univ. Carolin. 25 (1984), 368–370.
[2] Z. Frolík: Generalizations of the $G_\delta $-property of complete metric spaces. Czechoslovak Math. J. 10 (85) (1960), 359–379. MR 0116305
[3] Z. Frolík: A survey of separable descriptive theory of sets and spaces. Czechoslovak Math. J. 20 (1970), 406–467. MR 0266757
[4] Z. Frolík: Čech-analytic spaces (research announcement). Comment. Math. Univ. Carolin. 25 (1984), 367–368.
[5] R. W. Hansell: Descriptive Topology. Recent Progress in Recent Topology, North-Holland, Amsterdam, London, New York, Tokyo, 1992, pp. 275–315. MR 1229129 | Zbl 0805.54036
[6] R. W. Hansell: Descriptive sets and the topology of nonseparable Banach spaces. Serdica Math. J. 27 (2001), 1–66. MR 1828793 | Zbl 0982.46012
[7] R. W. Hansell: Compact perfect sets in weak analytic spaces. Topology Appl. 41 (1991), 65–72. DOI 10.1016/0166-8641(91)90101-Q | MR 1129699 | Zbl 0759.54016
[8] P. Holický: Čech analytic and almost $K$-descriptive spaces. Czechoslovak Math. J. 43 (1993), 451–466. MR 1249614
[9] P. Holický: Zdeněk Frolík and the descriptive theory of sets and spaces. Acta Univ. Carolin. Math. Phys. 32 (1991), 5–21. MR 1146762
[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
[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
[12] J. E. Jayne, I. Namioka and C. A. Rogers: Properties like the Radon-Nikodým property. Preprint. (1989).
[13] J. E. Jayne and C. A. Rogers: $K$-analytic sets. Analytic Sets, Academic Press, London, 1980, pp. 1–181. MR 0608794
[14] I. Namioka: Separate continuity and joint continuity. Pacific J. Math. 51 (1974), 515–531. DOI 10.2140/pjm.1974.51.515 | MR 0370466 | Zbl 0294.54010
[15] I. Namioka and R. Pol: $\sigma $-fragmentability and analyticity. Mathematika 43 (1996), 172–181. DOI 10.1112/S0025579300011670 | MR 1401716
[16] I. Namioka and R. Pol: $\sigma $-fragmentability of mappings into $C_p(K)$. Topology Appl. 89 (1998), 249–263. DOI 10.1016/S0166-8641(97)00217-4 | MR 1645164
Search
Partner of
