Space of Baire functions. I

J. E. Jayne

Annales de l'institut Fourier (1974)

  • Volume: 24, Issue: 4, page 47-76
  • ISSN: 0373-0956

Abstract

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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 α for each countable ordinal α . 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.

How to cite

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Jayne, J. E.. "Space of Baire functions. I." Annales de l'institut Fourier 24.4 (1974): 47-76. <http://eudml.org/doc/74203>.

@article{Jayne1974,
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.},
author = {Jayne, J. E.},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {4},
pages = {47-76},
publisher = {Association des Annales de l'Institut Fourier},
title = {Space of Baire functions. I},
url = {http://eudml.org/doc/74203},
volume = {24},
year = {1974},
}

TY - JOUR
AU - Jayne, J. E.
TI - Space of Baire functions. I
JO - Annales de l'institut Fourier
PY - 1974
PB - Association des Annales de l'Institut Fourier
VL - 24
IS - 4
SP - 47
EP - 76
AB - 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.
LA - eng
UR - http://eudml.org/doc/74203
ER -

References

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