Moors, W.B. & Somasundaram, S. (2002). A weakly Stegall space that is not a Stegall space. In Proceedings of the Mathematical Society, 131, 647-654.
Permanent Research Commons link: http://hdl.handle.net/10289/1269
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 φ : B2X, φ 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), weak) does not.
Department of Mathematics, University of Waikato
First published in Proceedings of the Mathematical Society in volume 131, pages 647-654, published by the American Mathematical Society. Copyright 2002, American Mathematical Society.