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Space of Baire functions. I

J. E. Jayne — 1974

Annales de l'institut Fourier

Several equivalent conditions are given for the existence of real-valued Baire functions of all classes on a type of K -analytic spaces, called disjoint analytic spaces, and on all pseudocompact spaces. The sequential stability index for the Banach space of bounded continuous real-valued functions on these spaces is shown to be either 0 , 1 , or Ω (the first uncountable ordinal). In contrast, the space of bounded real-valued Baire functions of class 1 is shown to contain closed linear subspaces with index...

Norm fragmented weak* compact sets.

J. E. Jayne;  I. Namioka;  C. A. Rogers — 1990

Collectanea Mathematica

A Banach space which is a Cech-analytic space in its weak topology has fourteen measure-theoretic, geometric and topological properties. In a dual Banach space with its weak-star topology essentially the same properties are all equivalent one to another.

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