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Sbornik: Mathematics, 2008, Volume 199, Issue 6, Pages 833–869
DOI: https://doi.org/10.1070/SM2008v199n06ABEH003944 (Mi sm3845) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Classification of Borel sets and functions for an arbitrary space

V. K. Zakharova, T. V. Rodionovb

a Centre for New Information Technologies, Moscow State University
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (517 kB) Citations (5)
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DOI: https://doi.org/10.1070/SM2008v199n06ABEH003944
Abstract: 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.
Received: 26.02.2007 and 04.10.2007
Russian version:
Matematicheskii Sbornik, 2008, Volume 199, Number 6, Pages 49–84
DOI: https://doi.org/10.4213/sm3845
Bibliographic databases:
UDC: 517.517+510.225+517.518.26
MSC: Primary 26A21; Secondary 54C50, 54H05, 03E15
Language: English
Original paper language: Russian
Citation: V. K. Zakharov, T. V. Rodionov, “Classification of Borel sets and functions for an arbitrary space”, Mat. Sb., 199:6 (2008), 49–84; Sb. Math., 199:6 (2008), 833–869
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/sm/v199/i6/p49
    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:88
    First page:8
     
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