Undetermined sets of point-open games

• Autorzy: Janusz Pawlikowski
• Języki publikacji: EN

Abstrakty

EN

We show that a set of reals is undetermined in Galvin's point-open game iff it is uncountable and has property C", which answers a question of Gruenhage.

Kategorie tematyczne

• 54G15: Pathological spaces
• 03E15: Descriptive set theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1994
• Tom: 144
• Numer: 3
• Strony: 279-285

Daty

wydano

1994

otrzymano

1993-04-27

poprawiono

1993-10-08

Twórcy

autor

Janusz Pawlikowski

• Department of Mathematics, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Bibliografia

• [AR] A. Andryszczak and I. Recław, A note on strong measure zero sets, to appear.
• [FM] D. H. Fremlin and A. 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.
• [GT] F. Galvin and R. Telgársky, Stationary strategies in topological games, Topology Appl. 22 (1986), 51-69.
• [K] K. Kuratowski, Topology, Vol. 1, Academic Press, 1966.
• [L] R. Laver, On the consistency of Borel's conjecture, Acta Math. 137 (1976), 151-169.
• [M] A. W. Miller, Special subsets of the real line, in: Handbook of Set-Theoretical Topology, K. Kunen and J. E. Vaughan (eds.), Elsevier, 1984, 203-233.
• [P] J. Pawlikowski, Property C", strongly meager sets and subsets of the plane, preprint.
• [R] I. Recław, Every Lusin set is undetermined in the point-open game, Fund. Math. 144 (1994), 43-54.
• [T] S. Todorčević, On the Lindelöf property of Aronszajn trees, in: General Topology and its Relation to Analysis and Algebra VI, Z. Frolí k (ed.), Heldermann-Verlag, 1988, 577-588.