ArticleOriginal scientific text

Title

Undetermined sets of point-open games

Authors 1

Affiliations

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

Abstract

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.

Bibliography

  1. [AR] A. Andryszczak and I. Recław, A note on strong measure zero sets, to appear.
  2. [FM] D. H. Fremlin and A. Miller, On some properties of Hurewicz, Menger, and Rothberger, Fund. Math. 129 (1988), 17-33.
  3. [G] F. Galvin, Indeterminacy of point-open games, Bull. Acad. Polon. Sci. 26 (1978), 445-449.
  4. [GT] F. Galvin and R. Telgársky, Stationary strategies in topological games, Topology Appl. 22 (1986), 51-69.
  5. [K] K. Kuratowski, Topology, Vol. 1, Academic Press, 1966.
  6. [L] R. Laver, On the consistency of Borel's conjecture, Acta Math. 137 (1976), 151-169.
  7. [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.
  8. [P] J. Pawlikowski, Property C", strongly meager sets and subsets of the plane, preprint.
  9. [R] I. Recław, Every Lusin set is undetermined in the point-open game, Fund. Math. 144 (1994), 43-54.
  10. [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.

Additional information

http://matwbn.icm.edu.pl/ksiazki/fm/fm144/fm14436.pdf

Pages:
279-285
Main language of publication
English
Received
1993-04-27
Accepted
1993-10-08
Published
1994
Exact and natural sciences