ArticleOriginal scientific text

Title

The functor σ²X

Authors 1, 2

Affiliations

  1. Department of Mathematics, University of Toronto, Toronto, Canada M5S 1A1
  2. Matematički Institut, Kneza Mihaila 35, 11000 Beograd, pp. 38, Yugoslavia

Abstract

We disprove the existence of a universal object in several classes of spaces including the class of weakly Lindelöf Banach spaces.

Bibliography

  1. S. Argyros and Y. Benyamini, Universal WCG Banach spaces and universal Eberlein compacts, Israel J. Math. 58 (1987), 305-320.
  2. S. Argyros and S. Mercourakis, Weakly Lindelöf Banach spaces, Rocky Mountain J. Math. 23 (1993), 395-446.
  3. Y. Benyamini, M. E. Rudin and M. Wage, Continuous images of weakly compact subsets of Banach spaces, Pacific J. Math. 70 (1977), 309-324.
  4. Y. Benyamini and T. Starbird, Embedding weakly compact sets into Hilbert space, Israel J. Math. 23 (1976), 137-141.
  5. H. H. Corson, The weak topology of a Banach space, Trans. Amer. Math. Soc. 101 (1961), 1-15.
  6. A. S. Esenin-Vol'pin, On the existence of universal bicompacta in a given weight, Dokl. Akad. Nauk SSSR 68 (1949), 649-652 (in Russian).
  7. V. V. Filippov, On perfectly normal bicompacta, Soviet Math. Dokl. 10 (1969), 1503-1507.
  8. A. M. Gleason and R. P. Dilworth, A generalized Cantor Theorem, Proc. Amer. Math. Soc. 13 (1962), 704-705.
  9. G. Gruenhage, On a Corson space of Todorčević, Fund. Math. 126 (1986), 261-268.
  10. S. P. Gul'ko, On the structure of spaces of continuous functions and their complete paracompactness, Russian Math. Surveys 34 (1979), 36-44.
  11. F. Hartogs, Über das Problem der Wohlordnung, Math. Ann. 76 (1915), 436-443.
  12. G. Kurepa, Ensembles ordonnés et leur sous-ensembles bien ordonnés, C. R. Acad. Sci. Paris 242 (1956), 2202-2203.
  13. A. G. Leiderman and G. A. Sokolov, Adequate families of sets and Corson compacta, Comment. Math. Univ. Carolin. 25 (1984), 233-245.
  14. R. Pol, On a question of H. H. Corson and some related problems, Fund. Math. 109 (1980), 143-154.
  15. D. B. Shakhmatov, Compact spaces and their generalizations, in: Recent Progress in Topology, M. Hušek and J. van Mill (eds.), Elsevier, 1992.
  16. W. Szlenk, The non-existence of a separable reflexive Banach space universal for all separable reflexive Banach spaces, Studia Math. 30 (1968), 53-61.
  17. M. Talagrand, Espaces de Banach faiblement K-analytiques, Ann. of Math. 110 (1979), 407-438.
  18. S. Todorčević, Partition relations for partially ordered sets, Acta Math. 155 (1985), 1-25.
  19. M. Valdivia, Resolutions of the identity in certain Banach spaces, Collect. Math. 39 (1988), 127-140.
  20. L. Vašak, On one generalization of weakly compactly generated Banach spaces, Studia Math. 70 (1981), 1-19.
  21. S. Watson and W. Weiss, A topology on the union of the double arrow space and the integers, Topology Appl. 28 (1988), 177-179.
  22. E. Zermelo, Beweis, das jede Menge wohlgeordnet werden kann, Math. Ann. 59 (1904), 514-516.
Pages:
49-57
Main language of publication
English
Received
1994-10-11
Accepted
1995-04-10
Published
1995
Exact and natural sciences