A weak Asplund space whose dual is not weak* fragmentable

摘要

Under the assumption that there exists in the unit interval [0, 1] an uncountable set A with the property that every continuous mapping from a Baire metric space B into A is constant on some non-empty open subset of B, we construct a Banach space X such that (X*; weak*) belongs to Stegall's class but (X*, weak*) is not fragmentable. [References: 8]