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1994 | 144 | 1 | 43-54
Tytuł artykułu

Every Lusin set is undetermined in the point-open game

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We show that some classes of small sets are topological versions of some combinatorial properties. We also give a characterization of spaces for which White has a winning strategy in the point-open game. We show that every Lusin set is undetermined, which solves a problem of Galvin.
Słowa kluczowe
Rocznik
Tom
144
Numer
1
Strony
43-54
Opis fizyczny
Daty
wydano
1994
otrzymano
1992-07-29
poprawiono
1993-05-15
Twórcy
  • Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland
Bibliografia
  • [B1] T. Bartoszyński, Additivity of measure implies additivity of category, Trans. Amer. Math. Soc. 281 (1984), 209-213.
  • [B2] T. Bartoszyński, Combinatorial aspects of measure and category, Fund. Math. 127 (1987), 225-239.
  • [BBM] R. H. Bing, W. W. Bledsoe and R. D. Mauldin, Sets generated by rectangles, Pacific J. Math. 51 (1974), 27-36.
  • [BRR] L. Bukovský, I. Recław and M. Repický, Spaces not distinguishing pointwise and quasinormal convergence of real functions, Topology Appl. 41 (1991), 25-40.
  • [D] E. K. van Douwen, The integers and topology, in: Handbook of Set-Theoretic Topology, K. Kunen and J. Vaughan (eds.), North-Holland, Amsterdam, 1984, 111-167.
  • [F] D. H. Fremlin, Cichoń's diagram in: Sém. Initiation à l'Analyse, G. Choquet, M. Rogalski, J. Saint-Raymond, Université Pierre et Marie Curie, Paris, 1983//84, no. 5, 13 pp.
  • [FJ] D. H. Fremlin and J. Jasiński, $G_δ$-covers and large thin sets of reals, Proc. London Math. Soc. (3) 53 (1986), 518-538.
  • [FM] D. H. Fremlin and A. W. Miller, On some properties of Hurewicz, Menger, and Rothberger, Fund. Math. 129 (1988), 17-33.
  • [G] F. Galvin, Indeterminacy of point-open games, Bull. Acad. Polon. Sci. 26 (1978), 445-449.
  • [GM] F. Galvin and A. W. Miller, γ-sets and other singular sets of real numbers, Topology Appl. 17 (1984), 145-155.
  • [M1] A. W. Miller, Special subsets of the real line, in: Handbook of Set-Theoretic Topology, K. Kunen and J. Vaughan (eds.), North-Holland, Amsterdam, 1984, 201-233.
  • [M2] A. W. Miller, Some properties of measure and category, Trans. Amer. Math. Soc. 266 (1981), 93-114; Corrections and additions, ibid. 271 (1982), 347-348.
  • [M3] A. W. Miller, Additivity of measure implies dominating reals, Proc. Amer. Math. Soc. 91 (1984), 111-117.
  • [M4] A. W. Miller, The Baire category theorem and cardinals of countable cofinality, J. Symbolic Logic 47 (1982), 275-287.
  • [M5] A. W. Miller, A characterization of the least cardinal for which Baire category theorem fails, Proc. Amer. Math. Soc. 86 (1982), 498-502.
  • [PR] J. Pawlikowski and I. Recław, On parametrized Cichoń's diagram, in preparation.
  • [R] I. Recław, On small sets in the sense of measure and category, Fund. Math. 133 (1989), 255-260.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv144i1p43bwm
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