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

DOI:
https://doi.org/10.1090/S0002-9939-04-07744-5

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, , where is a weak Asplund space such that (in the weak* topology) in not in Stegall's class, whereas 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:
https://doi.org/10.1090/S0002-9939-04-07744-5

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.