ArticleOriginal scientific text

Title

Fragmentability and σ-fragmentability

Authors 1, 2, 1

Affiliations

  1. Department of Mathematics, University College London, Gower Street, London WC1E 6BT, U.K.
  2. Department of Mathematics, GN-50, University of Washington, Seattle, Washington 98195, U.S.A.

Abstract

Recent work has studied the fragmentability and σ-fragmentability properties of Banach spaces. Here examples are given that justify the definitions that have been used. The fragmentability and σ-fragmentability properties of the spaces and c({Γ}), with Γ uncountable, are determined.

Bibliography

  1. G. Choquet, Lectures on Analysis, Vol. 1, Benjamin, New York, 1969.
  2. R. Engelking, General Topology, PWN, Warszawa, 1977.
  3. R. W. Hansell, J. E. Jayne and M. Talagrand, First class selectors for weakly upper semi-continuous multi-valued maps in Banach spaces, J. Reine Angew. Math. 361 (1985), 201-220 and 362 (1986), 219-220.
  4. R. Haydon and C. A. Rogers, A locally uniformly convex renorming for certain C(K), Mathematika 37 (1990), 1-8.
  5. J. E. Jayne, I. Namioka and C. A. Rogers, Norm fragmented weak compact sets, Collect. Math. 41 (1990), 133-163.
  6. J. E. Jayne, I. Namioka and C. A. Rogers, σ-Fragmented Banach spaces, Mathematika 39 (1992), 161-188 and 197-215.
  7. J. E. Jayne, I. Namioka and C. A. Rogers, Topological properties of Banach spaces, Proc. London Math. Soc. (3) 66 (1993), 651-672.
  8. J. E. Jayne, I. Namioka and C. A. Rogers, σ-Fragmented Banach spaces, II, preprint.
  9. J. E. Jayne and C. A. Rogers, Borel selectors for upper semi-continuous set-valued maps, Acta Math. 155 (1985), 41-79.
  10. J. E. Jayne, J. Orihuela, A. J. Pallarés and G. Vera, σ-Fragmentability of multivalued maps and selection theorems, J. Funct. Anal. 115 (1993).
  11. J. L. Kelley, General Topology, Springer, New York, 1975.
  12. I. Namioka, Radon-Nikodým compact spaces and fragmentability, Mathematika 34 (1987), 258-281.
  13. I. Namioka and R. Pol, Mappings of Baire spaces into function spaces and Kadec renorming, Israel J. Math. 78 (1992), 1-20.
  14. N. K. Ribarska, Internal characterization of fragmentable spaces, Mathematika 34 (1987), 243-257.
  15. N. K. Ribarska, A note on fragmentability of some topological spaces, C. R. Acad. Bulgare Sci. 43 (1990), 13-15.
  16. Z. Semadeni, Banach Spaces of Continuous Functions, Vol. 1, PWN, Warszawa, 1971.

Additional information

http://matwbn.icm.edu.pl/ksiazki/fm/fm143/fm14333.pdf

Pages:
207-220
Main language of publication
English
Received
1992-09-02
Accepted
1993-05-14
Published
1993
Exact and natural sciences