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Jayne, J. E.
Space of Baire functions. I. Annales de l'institut Fourier, 24 no. 4 (1974), p. 47-76
Full text djvu | pdf | Reviews MR 51 #6714 | Zbl 0287.46031

stable URL: http://www.numdam.org/item?id=AIF_1974__24_4_47_0

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Abstract

Several equivalent conditions are given for the existence of real-valued Baire functions of all classes on a type of ${\bf K}$-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 $\Omega $ (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 $\alpha $ for each countable ordinal $\alpha $. The sequential stability index for linear subspaces of continuous real-valued functions on a compact space is shown to be invariant under isomorphic embeddings in the space of continuous real-valued functions on any compact space.

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