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Mathematics of the USSR-Sbornik, 1981, Volume 38, Issue 2, Pages 201–216
DOI: https://doi.org/10.1070/SM1981v038n02ABEH001229 (Mi sm2442) 		 
This article is cited in 8 scientific papers (total in 8 papers)

The Banach–Mazur game

L. R. Lisagor
English version PDF (1000 kB) Citations (8)
References:
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DOI: https://doi.org/10.1070/SM1981v038n02ABEH001229
Abstract: The Banach–Mazur game is investigated on the set of all general recursive functions. The concept of the category of a set of general recursive functions is introduced. This concept is used to formulate and prove necessary and sufficient conditions for the existence of a winning strategy for one of the players in the Banach–Mazur game, the conditions in question being analogous to the theorems of Banach for the Banach–Mazur game on the set of real numbers. The concept of the measure of a set of general recursive functions is also introduced, and the relationship between this concept and the one of category is given.
Bibliography: 8 titles.
Received: 10.05.1978
Russian version:
Matematicheskii Sbornik. Novaya Seriya, 1979, Volume 110(152), Number 2(10), Pages 218–234
Bibliographic databases:
UDC: 518.9
MSC: Primary 90D05, 03F60; Secondary 03D99
Language: English
Original paper language: Russian
Citation: L. R. Lisagor, “The Banach–Mazur game”, Mat. Sb. (N.S.), 110(152):2(10) (1979), 218–234; Math. USSR-Sb., 38:2 (1981), 201–216
Citation in format AMSBIB
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\by L.~R.~Lisagor
\paper The Banach--Mazur game
\jour Mat. Sb. (N.S.)
\yr 1979
\vol 110(152)
\issue 2(10)
\pages 218--234
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=552112}
\zmath{https://zbmath.org/?q=an:0429.90102|0426.03044}
\transl
\jour Math. USSR-Sb.
\yr 1981
\vol 38
\issue 2
\pages 201--216
\crossref{https://doi.org/10.1070/SM1981v038n02ABEH001229}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1981LG68600003}
Linking options:
  • https://www.mathnet.ru/eng/sm2442
  • https://doi.org/10.1070/SM1981v038n02ABEH001229
  • https://www.mathnet.ru/eng/sm/v152/i2/p218
    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
    Statistics & downloads:
    Abstract page:612
    Russian version PDF:366
    English version PDF:24
    References:46
    First page:1
     
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