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Russian Mathematical Surveys, 2005, Volume 60, Issue 4, Pages 699–719
DOI: https://doi.org/10.1070/RM2005v060n04ABEH003674
(Mi rm1447)
 

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
References:
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
Russian version:
Uspekhi Matematicheskikh Nauk, 2005, Volume 60, Issue 4(364), Pages 123–144
DOI: https://doi.org/10.4213/rm1447
Bibliographic databases:
Document Type: Article
UDC: 515.128+515.12
MSC: Primary 54H05; Secondary 28A05, 54C10, 54D15, 54E52
Language: English
Original paper language: Russian
Citation: M. M. Choban, “On some problems of descriptive set theory in topological spaces”, Uspekhi Mat. Nauk, 60:4(364) (2005), 123–144; Russian Math. Surveys, 60:4 (2005), 699–719
Citation in format AMSBIB
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  • https://doi.org/10.1070/RM2005v060n04ABEH003674
  • https://www.mathnet.ru/eng/rm/v60/i4/p123
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Успехи математических наук Russian Mathematical Surveys
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    Abstract page:768
    Russian version PDF:324
    English version PDF:28
    References:99
    First page:1
     
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