Proceedings of the American Mathematical Society

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A weakly Stegall space that is not a Stegall space


Authors: Warren B. Moors and Sivajah Somasundaram
Journal: Proc. Amer. Math. Soc. 131 (2003), 647-654
MSC (2000): Primary 54C60, 26E25, 54C10
Published electronically: June 27, 2002
MathSciNet review: 1933358
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Abstract: A topological space $X$ is said to belong to the class of Stegall (weakly Stegall) spaces if for every Baire (complete metric) space $B$ and minimal usco $\varphi:B\rightarrow 2^{X}$, $\varphi$ is single-valued at some point of $B$. In this paper we show that under some additional set-theoretic assumptions that are equiconsistent with the existence of a measurable cardinal there is a Banach space $X$ whose dual, equipped with the weak$^*$ topology, is in the class of weakly Stegall spaces but not in the class of Stegall spaces. This paper also contains an example of a compact space $K$ such that $K$ belongs to the class of weakly Stegall spaces but $(C(K)^*,\mbox{weak$^*$ })$ does not.


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Additional Information

Warren B. Moors
Affiliation: Department of Mathematics, The University of Waikato, Private Bag 3105, Hamilton 2001, New Zealand
Email: moors@math.waikato.ac.nz

Sivajah Somasundaram
Affiliation: Department of Mathematics, The University of Waikato, Private Bag 3105, Hamilton 2001, New Zealand
Email: ss15@math.waikato.ac.nz

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06717-5
Keywords: Weak Asplund, almost weak Asplund, Stegall space, weakly Stegall space
Received by editor(s): September 12, 2001
Published electronically: June 27, 2002
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2002 American Mathematical Society