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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A weakly Stegall space that is not a Stegall space
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by Warren B. Moors and Sivajah Somasundaram PDF
Proc. Amer. Math. Soc. 131 (2003), 647-654 Request permission

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.
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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
  • 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