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A weak Asplund space whose dual is not weak$^*$ fragmentable


Authors: Petar S. Kenderov, Warren B. Moors and Scott Sciffer
Journal: Proc. Amer. Math. Soc. 129 (2001), 3741-3747
MSC (2000): Primary 54C60, 46B20, 54C10
DOI: https://doi.org/10.1090/S0002-9939-01-06002-6
Published electronically: May 21, 2001
MathSciNet review: 1860511
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Abstract:

Under the assumption that there exists in the unit interval $[0,1]$ an uncountable set $A$ with the property that every continuous mapping from a Baire metric space $B$into $A$ is constant on some non-empty open subset of $B$, we construct a Banach space $X$ such that $(X^*,\mbox{weak$^*$ })$ belongs to Stegall's class but $(X^*,\mbox{weak$^*$ })$is not fragmentable.


References [Enhancements On Off] (What's this?)

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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: https://doi.org/10.1090/S0002-9939-01-06002-6
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
Published electronically: 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
Article copyright: © Copyright 2001 American Mathematical Society

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