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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On subclasses of weak Asplund spaces


Authors: Ondrej F. K. Kalenda and Kenneth Kunen
Journal: Proc. Amer. Math. Soc. 133 (2005), 425-429
MSC (2000): Primary 46B26, 03E35
Published electronically: September 2, 2004
MathSciNet review: 2093063
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Abstract: Assuming the consistency of the existence of a measurable cardinal, it is consistent to have two Banach spaces, $X,Y$, where $X$ is a weak Asplund space such that $X^{*}$ (in the weak* topology) in not in Stegall's class, whereas $Y^{*}$is in Stegall's class but is not weak* fragmentable.


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Additional Information

Ondrej F. K. Kalenda
Affiliation: Department of Mathematical Analysis, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic
Email: kalenda@karlin.mff.cuni.cz

Kenneth Kunen
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Email: kunen@math.wisc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07744-5
PII: S 0002-9939(04)07744-5
Keywords: Weak Asplund space, fragmentable space, Stegall's class of spaces, measurable cardinal
Received by editor(s): October 4, 2001
Published electronically: September 2, 2004
Additional Notes: The first author was supported by Research grants GAUK 277/2001, GAČR 201/00/1466 and MSM 113200007
The second author was supported by NSF Grant DMS-0097881
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.