## A weakly Stegall space that is not a Stegall space

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- by Warren B. Moors and Sivajah Somasundaram
- Proc. Amer. Math. Soc.
**131**(2003), 647-654 - DOI: https://doi.org/10.1090/S0002-9939-02-06717-5
- Published electronically: June 27, 2002
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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 $(C(K)^*,\mathrm {weak}^*)$ does not.## References

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## Bibliographic 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
- Received by editor(s): September 12, 2001
- Published electronically: June 27, 2002
- Communicated by: Jonathan M. Borwein
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**131**(2003), 647-654 - MSC (2000): Primary 54C60, 26E25, 54C10
- DOI: https://doi.org/10.1090/S0002-9939-02-06717-5
- MathSciNet review: 1933358