Undetermined sets of point-open games

Janusz Pawlikowski

Fundamenta Mathematicae (1994)

  • Volume: 144, Issue: 3, page 279-285
  • ISSN: 0016-2736

Abstract

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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.

How to cite

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Pawlikowski, Janusz. "Undetermined sets of point-open games." Fundamenta Mathematicae 144.3 (1994): 279-285. <http://eudml.org/doc/212029>.

@article{Pawlikowski1994,
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.},
author = {Pawlikowski, Janusz},
journal = {Fundamenta Mathematicae},
keywords = {infinite game; Rothberger's properties; Menger's property; covering properties},
language = {eng},
number = {3},
pages = {279-285},
title = {Undetermined sets of point-open games},
url = {http://eudml.org/doc/212029},
volume = {144},
year = {1994},
}

TY - JOUR
AU - Pawlikowski, Janusz
TI - Undetermined sets of point-open games
JO - Fundamenta Mathematicae
PY - 1994
VL - 144
IS - 3
SP - 279
EP - 285
AB - 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.
LA - eng
KW - infinite game; Rothberger's properties; Menger's property; covering properties
UR - http://eudml.org/doc/212029
ER -

References

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  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. Zbl0665.54026
  3. [G] F. Galvin, Indeterminacy of point-open games, Bull. Acad. Polon. Sci. 26 (1978), 445-449. Zbl0392.90101
  4. [GT] F. Galvin and R. Telgársky, Stationary strategies in topological games, Topology Appl. 22 (1986), 51-69. Zbl0581.90108
  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. Zbl0357.28003
  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. Zbl0906.04001
  9. [R] I. Recław, Every Lusin set is undetermined in the point-open game, Fund. Math. 144 (1994), 43-54. Zbl0809.04002
  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. 

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