The Lindelöf property and σ-fragmentability

Fundamenta Mathematicae

Volumn 180, Issue 2, 2003, Pages 161-183

  Cascales, B ^a,b   Namioka, I ^a,c  

^a Universidad de Murcia ^*

^b UNIVERSITY OF MURCIA   (Spain)

^c UNIVERSITY OF WASHINGTON   (United States)

Author keywords

Compact perfect sets; Corson compact spaces; K analytic spaces; Lindel f spaces; topology; fragmentability

Indexed keywords

EID: 1942506071     PISSN: 00162736     EISSN: None     Source Type: Journal    
DOI: 10.4064/fm180-2-3     Document Type: Article

References (28)

1. K. Alster, Some remarks on Eberlein compacts, Fund. Math. 104 (1979), 43-46.
2. K. Alster and R. Pol, On function spaces of compact subspaces of Σ-products of the real line, ibid. 107 (1980), 135-143.
3. A. V. Arkhangel'skiǐ, Topological Function Spaces, Math. Appl. (Soviet Series) 78, Kluwer, Dordrecht, 1992, translated from the Russian by R. A. M. Hoksbergen.
4. δ-topology and K-analytic spaces without perfect compact sets, Colloq. Math. 58 (1990), 189-199.
5. B. Cascales, G. Manjabacas and G. Vera, Fragmentability and compactness in C(K)spaces, Studia Math. 131 (1998), 73-87.
6. B. Cascales, I. Namioka and J. Orihuela, The Lindelöf property in Banach spaces, ibid. 154 (2003), 165-192.
7. B. Cascales, I. Namioka and G. Vera, The Lindelöf property and fragmentability, Proc. Amer. Math. Soc. 128 (2000), 3301-3309.
8. 0(Γ), Bull. Polish Acad. Sci. Math. 32 (1984), 681-688.
9. G. A. Edgar, Measurability in a Banach space. II, Indiana Univ. Math. J. 28 (1979), 559-579.
10. G. Godefroy and M. Talagrand, Espaces de Banach représentables, Israel J. Math. 41 (1982), 321-330.
11. S. P. Gul'ko, On properties of subsets of σ-products, Soviet Math. Dokl. 18 (1977), 1438-1442.
12. J. E. Jayne, I. Namioka and C. A. Rogers, Topological properties of Banach spaces, Proc. London Math. Soc. (3) 66 (1993), 651-672.
13. O. F. K. Kalenda, Valdivia compact spaces in topology and Banach space theory, Extracta Math. 15 (2000), 1-85.
14. p(X), J. Math. Anal. Appl. 280 (2003), 155-162.
15. J. L. Kelley, General Topology, Grad. Texts in Math. 27, Springer, New York, 1975, reprint of the 1955 edition [Van Nostrand, New York].
16. J. L. Kelley and I. Namioka, Linear Topological Spaces, Grad. Texts in Math. 36, Springer, New York, 1976. 2nd corrected printing.
17. A. W. Miller, Special subsets of the real line, in: Handbook of Set-Theoretic Topology, North-Holland, Amsterdam, 1984, 201-233.
18. I. Namioka, Radon-Nikodým compact spaces and fragmentability, Mathematika 34 (1987), 258-281.
19. I. Namioka and R. Pol, σ-fragmentability and analyticity, ibid. 43 (1996), 172-181.
20. N. Noble, Products with closed projections II, Trans. Amer. Math. Soc. 160 (1971), 169-183.
21. p(X)) = ω do not imply countable network weight in X, Acta Math. Hungar. 90 (2001), 119132.
22. J. Orihuela, Pointwise compactness in spaces of continuous functions, J. London Math. Soc. (2) 36 (1987), 143-152.
23. _, On weakly Lindelöf Banach spaces, in: Progress in Functional Analysis, North-Holland Math. Stud. 170, North-Holland, Amsterdam, 1992, 279-291.
24. R. Pol, A function space C(K) which is weakly Lindelöf but not weakly compactly generated, Studia Math. 64 (1979), 279-285.
25. _, On a question of H. H. Corson and some related problems, Fund. Math. 109 (1980), 143-154.
26. C. A. Rogers and J. E. Jayne, Analytic Sets, Chapter: K-analytic sets, Academic Press, 1980, 1-181.
27. M. Talagrand, Espaces de Banach faiblement script K sign-analytiques, Ann. of Math. (2) 110 (1979), 407-438.
28. J. van Mill, The Infinite-Dimensional Topology of Function Spaces, North-Holland Math. Library 64, North-Holland, Amsterdam, 2001.