Geodesic
Classification of Borel sets and functions for an arbitrary space
Sbornik. Mathematics, Tome 199 (2008) no. 6, pp. 833-869

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For Borel functions on a perfect normal space and a perfect topological space there are two Baire convergence classifications: one due to Lebesgue and Hausdorff and the other due to Banach. However, neither classification is valid for an arbitrary topological space. In this paper the Baire convergence classification of Borel functions on an arbitrary space is given. This classification of Borel functions uses two classifications of Borel sets: one generalises the Young-Hausdorff classification for a perfect space and the other is new. Bibliography: 17 titles. 
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     author = {V. K. Zakharov and T. V. Rodionov},
     title = {Classification of {Borel} sets and functions for an arbitrary space},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2008_199_6_a2/}
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V. K. Zakharov; T. V. Rodionov. Classification of Borel sets and functions for an arbitrary space. Sbornik. Mathematics, Tome 199 (2008) no. 6, pp. 833-869. http://geodesic.mathdoc.fr/item/SM_2008_199_6_a2/