Network characterization of Gul'ko compact spaces and their relatives

Journal of Mathematical Analysis and Applications

Volumn 297, Issue 2, 2004, Pages 791-811

  Garcia F ^a   Oncina, Luis ^a   Orihuela, Jose ^a  

^a UNIVERSITY OF MURCIA   (Spain)

Author keywords

Covering properties; Gul'ko compact; Network

Indexed keywords

EID: 4444307700     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmaa.2004.05.013     Document Type: Article

References (45)

1. Amir D. Lindenstrauss J. The structure of weakly compact sets in Banach spaces Ann. of Math. 88 1968 34-46
2. Argyros S. Arvanitakis A. A characterization of regular averaging operators and its consequences, Preprint, 2003
3. Argyros S. Mercourakis S. On weakly Lindelöf Banach spaces Rocky Mountain J. Math. 23 1993 395-446
4. Argyros S. Mercourakis S. Examples concerning heredity problems of WCG Banach spaces, 2003
5. Argyros S. Mercourakis S. Negrepontis S. Functional-analytic properties of Corson-compact spaces Studia Math. 89 1988 197-229
6. Arkangel'skii A.V. Topological Function Spaces 1992 Kluwer Academic Dordrecht
7. Burke D.K. Covering properties Handbook of Set-Theoretic Topology 1984 347-422 Elsevier
8. Cascales B. Namioka I. Orihuela J. The Lindelöf property in Banach spaces Studia Math. 154 2003 165-192
9. Cascales B. Orihuela J. A sequential property of set-valued maps J. Math. Anal. Appl. 156 1991 86-100
10. Corson H.H. Normality in subsets of product space Amer. J. Math. 81 1959 137-141
11. Deville R. Godefroy G. Zizler V. Smoothness and Renormings in Banach Spaces Pitman Monographs and Surveys in Pure and Applied Mathematics vol. 64 1993
12. Dow A. Junnila H. Pelant J. Weak covering properties of weak topologies Proc. London Math. Soc. (3) 75 1997 349-368
13. Dow A. Junnila H. Pelant J. Covering, networks and weak topologies, Preprint, 2004
14. Engelking R. General Topology 1977 PWN
15. Fabian M. Gâteaux Differentiability of Convex Functions and Topology. Weak Asplund Spaces 1997 Wiley
16. Fabian M. Godefroy G. Montesinos V. Zizler V. Inner characterizations of weakly compactly generated Banach spaces and their relatives, Preprint
17. Fabian M. Habala P. Hájek P. Montesinos Santalucía V. Pelant J. Zizler V. Functional Analysis and Infinite-Dimensional Geometry in: CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC vol. 8 2001 Springer-Verlag New York
18. Γ) Fund. Math. 128 1987 15-28
19. Godefroy G. Banach spaces of continuous functions on compact spaces Recent Progress in General Topology, II 2002 177-199 North-Holland Amsterdam
20. 2\Δ, W-sets, and compact subsets of Σ-products Topology Appl. 17 1984 287-304
21. Gruenhage G. Generalized metric spaces Handbook of Set-Theoretic Topology 1984 423-501 North-Holland
22. Gruenhage G. On a Corson compact space of Todorčević Fund. Math. 126 1986 261-268
23. Gruenhage G. A note on Gul'ko compact spaces Proc. Amer. Math. Soc. 100 1987 371-376
24. Gruenhage G. Michael E. A result on shrinkable open covers Topology Proc. 8 1983 37-43
25. Gul'ko S.P. Properties of sets that lie in Σ-products Dokl. Akad. Nauk SSSR 237 1977 505-508
26. Gul'ko S.P. The structure of spaces of continuous functions and their hereditary paracompactness Uspekhi Mat. Nauk 34 1979 33-40
27. Hansell R.W. Descriptive sets and the topology of nonseparable Banach spaces Serdica Math. J. 27 2001 1-66
28. Kechris A.S. Classical Descriptive Set Theory 1995 Springer-Verlag
29. Mercourakis S. On weakly countably determined Banach spaces Trans. Amer. Math. Soc. 300 1987 307-327
30. Mercourakis S. Negrepontis S. Banach spaces and topology II Hušec M. van Mill J. Recent Progress in General Topology 1992 493-536 Elsevier
31. Moltó A. Orihuela J. Troyanski S. Valdivia M. On weakly locally uniformly rotund Banach spaces J. Funct. Anal. 163 1999 252-271
32. Moltó A. Orihuela J. Troyanski S. Valdivia M. A nonlinear transfer technique, Preprint, 2003
33. Negrepontis S. Banach spaces and topology Handbook of Set-Theoretic Topology 1984 1045-1142 North-Holland
34. Oncina L. A new characterization of Eberlein compacta Studia Math. 146 1 2001 69-81
35. Oncina L. On WCG Asplund Banach spaces Quart. J. Math. 2004 in press
36. Oncina L. Raja M. Descriptive compact spaces and renorming Studia Math. 2004 in press
37. Orihuela J. Pointwise compactness in spaces of continuous functions J. London Math. Soc. (2) 36 1987 143-152
38. Orihuela J. On weakly Lindelöf Banach spaces Progress in Functional Analysis (Peñí scola, 1990), vol. 170 1992 279-291 North-Holland Amsterdam
39. Orihuela J. Schachermayer W. Valdivia M. Every Radon-Nikodym Corson compact space is Eberlein compact Studia Math. 98 1991 157-174
40. Rosenthal H.P. The heredity problem for weakly compactly generated Banach spaces Compositio Math. 28 1974 83-111
41. Sokolov G.A. On some classes of compact spaces lying in σ-products Comment. Math. Univ. Carolin. 25 1984 219-231
42. Talagrand M. Espaces de Banach faiblement K-analytiques Ann. of Math. 110 1979 407-438
43. Talagrand M. A new countably determined Banach space Israel J. Math. 47 1984 75-80
44. Valdivia M. Projective resolution of identity in C(K) spaces Arch. Math. 54 1990 493-498
45. Vašák L. On one generalization of weakly compactly generated Banach spaces Studia Math. 70 1981 11-19