A classification of separable Rosenthal compacta and its applications

Dissertationes Mathematicae

Volumn , Issue 449, 2008, Pages 5-52

  Argyros, S A ^a   Dodos, P ^a   Kanellopoulos, V ^a  

^a NATIONAL TECHNICAL UNIVERSITY OF ATHENS   (Greece)

Author keywords

Baire class one functions; Chains and antichains of trees; Characters of points in topological spaces; Compact spaces; Hereditarily separable spaces; Non separable Banach spaces; Ramsey theory; Sequential compactness; Trees; Unconditional families

Indexed keywords

EID: 84858778509     PISSN: 00123862     EISSN: 17306310     Source Type: Journal    
DOI: 10.4064/dm449-0-1     Document Type: Article

References (40)

1. P. Alexandroff and P. Urysohn, Memoire sur les espaces topologiques cornpacts dédié à Monsieur D. Egoroff, Verh. Akad. Wetensch, Amsterdam 14 (1929), no. 1.
2. S. A. Argyros, A. D. Arvanitakis and A. G. Tolias, Saturated extensions, the attractors method and hereditarily James tree spaces, in: Methods in Banach Spaces, J. M. F. Castillo and W. B. Johnson (eds,), London Math. Soc. Lecture Note Ser. 337, Cambridge Univ. Press, 2006, 1-90.
3. S. A. Argyros, P. Dodos and V. Kanellopoulos, Tree structures associated to a family of functions, J. Symbolic Logic 70 (2005), 681-695.
4. S. A. Argyros, P. Dodos and V. Kanellopoulos, Unconditional families in Banach spaces, Math. Ann., to appear.
5. S. A. Argyros, V. Felouzis and V. Kanellopoulos, A proof of Halpem-Lâuchli partition theorem, European J. Combin. 23 (2002), 1-10.
6. S. A. Argyros, G. Godefroy and H. P. Rosenthal, Descriptive set theory and Banach spaces, in: Handbook of the Geometry of Banach Spaces, Vol. 2, W. B. Johnson and J. Lindenstrauss (eds.), Elsevier, 2003, 1007-1069.
7. S. A. Argyros and A. Tolias, Methods in the theory of hereditarily indecomposable Banach spaces, Mem. Amer. Math. Soc. 170 (2004), no. 806.
8. A. Blass, A partition for perfect sets, Proc. Amer. Math. Soc. 82 (1981), 271-277.
9. J. Bourgain, On convergent seauences of continuous functions, Bull, Soc. Math. Belg. 32 (1980), 235-249.
10. J. Bourgain, D. H. Fremlin and M. Talagrand, Pointwise compact sets of Bairerrieasurable functions, Amer. J. Math. 100 (1978), 845-886.
11. G. Debs, Effective properties in compact sets of Borel functions, Mathematika 34 (1987), 64-68.
12. P. Dodos, Codings of separable compact subsets of the first Baire class, Ann. Pure Appl. Logic 142 (2006), 425-441.
13. R. Engelking, General Topology, Sigma Ser. Pure Math. 6, Heldermann, Berlin, 1989.
14. 1 d'apres H. P. Rosenthal, in: Sém. Maurey-Schwartz, École Polytechnique, 1973-74, exp, no. 26.
15. G. Godefroy, Cornpacts de Rosenthal, Pacific J. Math. 91 (1980), 293-306.
16. G. Godefroy and A. Louveau, Axioms of determinacy and biorthogonal systems, Israel J. Math. 67 (1989), 109-116.
17. G. Godefroyet M. Talagrand, Espaces de Banach représentables, ibid, 41 (1982), 321-330.
18. J. D. Halpern and H. Läuchli, A partition theorem, Trans. Amer. Math. Soc. 124 (1966), 360-367.
19. V. Kanellopoulos, Ramsey families of subtrees of the dyadic tree, ibid. 357 (2005), 3865-3886.
20. A. S. Kechris, Classical Descriptive Set Theory, Grad. Texts in Math. 156, Springer, 1995.
21. A. S. Kechris and A. Louveau, A classifîcation of Baire class 1 functions, Trans. Amer. Math. Soc. 318 (1990), 209-236.
22. A. Krawczyk, Rosenthal compacta and analytic sets, Proc. Amer. Math. Soc. 115 (1992), 1095-1100.
23. A. Louveau, S. Shelah and B. Veličković, Borel partitions of infinite subtrees of a perfect tree, Ann. Pure Appl. Logic 63 (1993), 271-281.
24. W. Marciszewski, On a classifîcation of pointwise compact sets of the first Baire class functions, Fund. Math. 133 (1989), 195-209.
25. A. W. Miller, infinite combinatorics and definability, Ann. Pure Appl. Logic 41 (1989), 179-203.
26. K. Milliken, Ramsey's theorem with sums and unions, J. Combin. Theory Ser. A 18 (1975), 276-290.
27. K. Milliken, A partition theorem for the infinite subtrees of a tree, Trans. Amer. Math. Soc. 263 (1981), 137-148.
28. E. Odell, Applications of Ramsey theorems to Banach space theory, in: Notes in Banach Spaces, Univ. Texas Press, 1980, 379-404.
29. J. Pawlikowski, Parametrized Ellentuck theorem, Topology Appl. 37 (1990), 65-73.
30. R. Pol, On pointwise and weak topology in function spaces, preprint 4/84, Warsaw Univ., 1984.
31. R. Pol, Note on compact sets of first Baire class functions, Proc. Amer. Math. Soc. 96 (1986), 152-154.
32. R. Pol, Note on pointwise convergence of sequences of analytic sets, Mathematika 36 (1989), 290-300.
33. 1, Proc. Nat, Acad, Sci. U.S.A. 71 (1974), 2411-2413.
34. H. P. Rosenthal, Point-wise compact subsets of the first Baire class, Amer. J. Math. 99 (1977), 362-378.
35. J. H. Silver, Every analytic set is Ramsey, J. Symbolic Logic 35 (1970), 60-64.
36. C. Stegall, The Radon-Nikodym property in conjugate Banach spaces, Trans. Amer. Math. Soc. 206 (1975), 213-223.
37. J. Stern, A Ramsey theorem for trees with an application to Banach spaces, Israel J. Math. 29 (1978), 179-188.
38. S. Todorčević, Compact subsets of the first Baire class, J. Amer. Math. Soc. 12 (1999), 1179-1212.
39. S. Todorčević, Introduction to Ramsey Spaces, to appear.
40. S. Todorčević, E-mail communication.