Fragmentability and σ-fragmentability

J. Jayne; I. Namioka; C. Rogers

Fundamenta Mathematicae (1993)

  • Volume: 143, Issue: 3, page 207-220
  • ISSN: 0016-2736

Abstract

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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 ℓ ∞ and ℓ c ∞ ( Γ ) , with Γ uncountable, are determined.

How to cite

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Jayne, J., Namioka, I., and Rogers, C.. "Fragmentability and σ-fragmentability." Fundamenta Mathematicae 143.3 (1993): 207-220. <http://eudml.org/doc/212005>.

@article{Jayne1993,
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 $ℓ^∞$ and $ℓ_c^∞(\{Γ\})$, with Γ uncountable, are determined.},
author = {Jayne, J., Namioka, I., Rogers, C.},
journal = {Fundamenta Mathematicae},
keywords = {fragmentability},
language = {eng},
number = {3},
pages = {207-220},
title = {Fragmentability and σ-fragmentability},
url = {http://eudml.org/doc/212005},
volume = {143},
year = {1993},
}

TY - JOUR
AU - Jayne, J.
AU - Namioka, I.
AU - Rogers, C.
TI - Fragmentability and σ-fragmentability
JO - Fundamenta Mathematicae
PY - 1993
VL - 143
IS - 3
SP - 207
EP - 220
AB - 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 $ℓ^∞$ and $ℓ_c^∞({Γ})$, with Γ uncountable, are determined.
LA - eng
KW - fragmentability
UR - http://eudml.org/doc/212005
ER -

References

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  1. [1] G. Choquet, Lectures on Analysis, Vol. 1, Benjamin, New York, 1969. 
  2. [2] R. Engelking, General Topology, PWN, Warszawa, 1977. 
  3. [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. Zbl0573.54012
  4. [4] R. Haydon and C. A. Rogers, A locally uniformly convex renorming for certain C(K), Mathematika 37 (1990), 1-8. Zbl0725.46008
  5. [5] J. E. Jayne, I. Namioka and C. A. Rogers, Norm fragmented weak compact sets, Collect. Math. 41 (1990), 133-163. Zbl0764.46015
  6. [6] J. E. Jayne, I. Namioka and C. A. Rogers, σ-Fragmented Banach spaces, Mathematika 39 (1992), 161-188 and 197-215. 
  7. [7] J. E. Jayne, I. Namioka and C. A. Rogers, Topological properties of Banach spaces, Proc. London Math. Soc. (3) 66 (1993), 651-672. Zbl0793.54026
  8. [8] J. E. Jayne, I. Namioka and C. A. Rogers, σ-Fragmented Banach spaces, II, preprint. 
  9. [9] J. E. Jayne and C. A. Rogers, Borel selectors for upper semi-continuous set-valued maps, Acta Math. 155 (1985), 41-79. Zbl0588.54020
  10. [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). Zbl0822.54018
  11. [11] J. L. Kelley, General Topology, Springer, New York, 1975. 
  12. [12] I. Namioka, Radon-Nikodým compact spaces and fragmentability, Mathematika 34 (1987), 258-281. Zbl0654.46017
  13. [13] I. Namioka and R. Pol, Mappings of Baire spaces into function spaces and Kadec renorming, Israel J. Math. 78 (1992), 1-20. Zbl0794.54036
  14. [14] N. K. Ribarska, Internal characterization of fragmentable spaces, Mathematika 34 (1987), 243-257. Zbl0645.46017
  15. [15] N. K. Ribarska, A note on fragmentability of some topological spaces, C. R. Acad. Bulgare Sci. 43 (1990), 13-15. Zbl0763.54021
  16. [16] Z. Semadeni, Banach Spaces of Continuous Functions, Vol. 1, PWN, Warszawa, 1971. 

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