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A weak Asplund space whose dual is not weak fragmentable
Author(s):
Petar
S.
Kenderov;
Warren
B.
Moors;
Scott
Sciffer
Journal:
Proc. Amer. Math. Soc.
129
(2001),
3741-3747.
MSC (2000):
Primary 54C60, 46B20, 54C10
Posted:
May 21, 2001
MathSciNet review:
1860511
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Abstract:
Under the assumption that there exists in the unit interval ![$[0,1]$](/proc/2001-129-12/S0002-9939-01-06002-6/gif-abstract0/img1.gif) an uncountable set  with the property that every continuous mapping from a Baire metric space  into  is constant on some non-empty open subset of  , we construct a Banach space  such that  belongs to Stegall's class but  is not fragmentable.
References:
-
- 1.
- G. Bachman and L. Narici, Functional Analysis, Academic Press, 1966. MR 36:638
- 2.
- M. Fabian, Gâteaux Differentiability of Convex Functions: Weak Asplund Spaces, John Wiley and Sons, 1997. MR 98h:46009
- 3.
- R. Frankiewicz and K. Kunen, Solution of Kuratowski's problem on functions having the Baire property I, Fund. Math. 128 (1987), 171-180. MR 89a:03090
- 4.
- O. Kalenda, Stegall compact spaces which are not fragmentable, Topology Appl. 96 (1999), 121-132. MR 2000i:54027
- 5.
- P. S. Kenderov and J. Orihuela, A generic factorization theorem, Mathematika 42 (1995), 56-66. MR 96h:54014
- 6.
- W. B. Moors and S. D. Sciffer, Sigma-fragmentable spaces that are not countable unions of fragmentable subspaces, Topology Appl. (to appear.)
- 7.
- I. Namioka and R. Pol, Mappings of Baire spaces into function spaces and Kadec renorming, Israel J. Math. 78 (1992), 1-20. MR 94f:46020
- 8.
- C. Stegall, A class of topological spaces and differentiation of functions on Banach spaces, Vorlesungen aus dem Fachbereich Mathematik der Universität Essen 10 (1983), 63-77. MR 85j:46026
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Additional Information:
Petar
S.
Kenderov
Affiliation:
Institute of Mathematics, Bulgarian Academy of Science, Acad. G. Bonchev Street, Block 8, 1113 Sofia, Bulgaria
Email:
pkend@bgcict.acad.bg; pkend@math.bas.bg
Warren
B.
Moors
Affiliation:
Department of Mathematics, University of Waikato, Private Bag 3105, Hamilton, New Zealand
Email:
moors@math.auckland.ac.nz
Scott
Sciffer
Affiliation:
Department of Mathematics, University of Newcastle, Newcastle NSW-2308, Australia
DOI:
10.1090/S0002-9939-01-06002-6
PII:
S 0002-9939(01)06002-6
Keywords:
Stegall's class,
fragmentability,
weak Asplund space,
double arrow space,
Baire space,
minimal usco.
Received by editor(s):
February 17, 2000
Received by editor(s) in revised form:
April 22, 2000
Posted:
May 21, 2001
Additional Notes:
The first author was partially supported by Grant MM-701/97 of the National Fund for Scientific Research of the Bulgarian Ministry of Education, Science and Technology
The second author was supported by a Marsden fund grant, VUW 703, administered by the Royal Society of New Zealand
Communicated by:
Jonathan M. Borwein
Copyright of article:
Copyright
2001,
American Mathematical Society
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