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This article is cited in 4 scientific papers (total in 4 papers)
On some problems of descriptive set theory in topological spaces
M. M. Choban Tiraspol State University
Abstract:
Problems concerning the structure of Borel sets, their classification, and invariance of certain properties of sets under maps of given types arose in the first half of the previous century in the works of A. Lebesgue, R. Baire, N. N. Luzin, P. S. Alexandroff, P. S. Urysohn, P. S. Novikov, L. V. Keldysh, and A. A. Lyapunov and gave rise to many investigations. In this paper some results related to questions of F. Hausdorff, Luzin, Alexandroff, Urysohn, M. Katětov, and A. H. Stone are obtained. In 1934 Hausdorff posed the problem of invariance of the property of being an absolute $B$-set (that is, a Borel set in some complete separable metric space) under open continuous maps. By a theorem of Keldysh, the answer to this question is negative in general. The present paper gives additional conditions under which the answer to Hausdorff's question is positive. Some general problems of the theory of operations on sets are also treated.
Received: 11.05.2005
Citation:
M. M. Choban, “On some problems of descriptive set theory in topological spaces”, Russian Math. Surveys, 60:4 (2005), 699–719
Linking options:
https://www.mathnet.ru/eng/rm1447https://doi.org/10.1070/RM2005v060n04ABEH003674 https://www.mathnet.ru/eng/rm/v60/i4/p123
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Abstract page: | 771 | Russian version PDF: | 324 | English version PDF: | 28 | References: | 99 | First page: | 1 |
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