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A weak Asplund space whose dual is not weak fragmentable

Authors:	Petar S. Kenderov Warren B. Moors Scott Sciffer

Affiliation:	Institute of Mathematics, Bulgarian Academy of Science, Acad. G. Bonchev Street, Block 8, 1113 Sofia, Bulgaria ; Department of Mathematics, University of Waikato, Private Bag 3105, Hamilton, New Zealand ; Department of Mathematics, University of Newcastle, Newcastle NSW-2308, Australia

Abstract:	Under the assumption that there exists in the unit interval an uncountable set with the property that every continuous mapping from a Baire metric space into is constant on some non-empty open subset of , we construct a Banach space such that $(X^,mbox{weak$^$ })$ belongs to Stegall's class but $(X^,mbox{weak$^$ })$ is not fragmentable.

Keywords:	Stegall's class fragmentability weak Asplund space double arrow space Baire space minimal usco.

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