Geodesic
Classification of Borel sets and functions for an arbitrary space
Sbornik. Mathematics, Tome 199 (2008) no. 6, pp. 833-869 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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/

[1] H. Lebesgue, “Sur les fonctions représentables analytiquement”, Journ. de Math. (6), 1 (1905), 139–216 | Zbl

[2] F. Hausdorff, Grundzüge der Mengenlehre, Veit, Leipzig, 1914 | MR | Zbl

[3] F. Hausdorff, Set theory, Chelsea, New York, 1991 | MR | Zbl

[4] K. Kuratowski, Topology, vol. 1, Academic Press, New York–London, 1966 | MR | MR | Zbl | Zbl

[5] W. H. Young, “On functions and their associated sets of points”, Proc. London Math. Soc. (2), 12:1 (1913), 260–287 | DOI | Zbl

[6] H. R. Shatery, J. Zafarani, “The equality between Borel and Baire classes”, Real Anal. Exchange, 30:1 (2004), 373–384 | MR | Zbl

[7] S. Banach, “Über analytisch darstellbare Operationen in abstrakten Räumen”, Fund. Math., 17 (1931), 283–295 | Zbl

[8] V. K. Zakharov, “Borel cover and Borel extension”, Studia Sci. Math. Hungar., 24:4 (1989), 407–428 | MR | Zbl

[9] V. K. Zakharov, “Classification of Borel sets and functions for an arbitrary space”, Russian Acad. Sci. Dokl. Math., 66:1 (2002), 99–101 | MR | Zbl

[10] V. K. Zakharov, “Classification of Borel sets and functions in the general case”, Russian Math. Surveys, 57:4 (2002), 822–823 | DOI | MR | Zbl

[11] Th. Jech, Set theory, Springer Monogr. Math., Springer-Verlag, Berlin, 2003 | MR | Zbl

[12] V. K. Zakharov, “Connections between the Lebesgue extension and the Borel extension of the first class, and between the preimages corresponding to them”, Math. USSR-Izv., 37:2 (1991), 273–302 | DOI | MR | Zbl

[13] A. D. Alexandroff, “Additive set-functions in abstract spaces”, Matem. sb., 8(50):2 (1940), 307–348 ; 9(51):3 (1941), 563–628 ; 13(55):2–3 (1943), 169–238 | MR | Zbl | MR | Zbl | MR | Zbl

[14] V. K. Zakharov, A. V. Koldunov, “The characterization of the $\sigma$-covering of a compact space”, Siberian Math. J., 23:6 (1982), 834–841 | DOI | MR | Zbl

[15] V. K. Zaharov, A. V. Koldunov, “Characterization of the $\sigma$-cover of a compact”, Math. Nachr., 107:1 (1982), 7–16 | DOI | MR | Zbl

[16] S. M. Srivastava, A course on Borel sets, Grad. Texts in Math., 180, Springer-Verlag, New York, 1998 | MR | Zbl

[17] M. I. Dyachenko, P. L. Ulyanov, Mera i integral, Faktorial, M., 1998