Universally Kuratowski–Ulam Spaces And Open-Open Games

Piotr Kalemba; Andrzej Kucharski

Annales Mathematicae Silesianae (2015)

  • Volume: 29, Issue: 1, page 85-92
  • ISSN: 0860-2107

Abstract

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We examine the class of spaces in which the second player has a winning strategy in the open-open game. We show that this spaces are not universally Kuratowski–Ulam. We also show that the games G and G7 introduced by P. Daniels, K. Kunen, H. Zhou [Fund. Math. 145 (1994), no. 3, 205–220] are not equivalent.

How to cite

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Piotr Kalemba, and Andrzej Kucharski. "Universally Kuratowski–Ulam Spaces And Open-Open Games." Annales Mathematicae Silesianae 29.1 (2015): 85-92. <http://eudml.org/doc/276861>.

@article{PiotrKalemba2015,
abstract = {We examine the class of spaces in which the second player has a winning strategy in the open-open game. We show that this spaces are not universally Kuratowski–Ulam. We also show that the games G and G7 introduced by P. Daniels, K. Kunen, H. Zhou [Fund. Math. 145 (1994), no. 3, 205–220] are not equivalent.},
author = {Piotr Kalemba, Andrzej Kucharski},
journal = {Annales Mathematicae Silesianae},
keywords = {II-favorable space; uK-U space; tiny sequence},
language = {eng},
number = {1},
pages = {85-92},
title = {Universally Kuratowski–Ulam Spaces And Open-Open Games},
url = {http://eudml.org/doc/276861},
volume = {29},
year = {2015},
}

TY - JOUR
AU - Piotr Kalemba
AU - Andrzej Kucharski
TI - Universally Kuratowski–Ulam Spaces And Open-Open Games
JO - Annales Mathematicae Silesianae
PY - 2015
VL - 29
IS - 1
SP - 85
EP - 92
AB - We examine the class of spaces in which the second player has a winning strategy in the open-open game. We show that this spaces are not universally Kuratowski–Ulam. We also show that the games G and G7 introduced by P. Daniels, K. Kunen, H. Zhou [Fund. Math. 145 (1994), no. 3, 205–220] are not equivalent.
LA - eng
KW - II-favorable space; uK-U space; tiny sequence
UR - http://eudml.org/doc/276861
ER -

References

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  1. [1] Bartoszyński T., Combinatorial aspects of measure and category, Fund. Math. 127 (1987), no. 3, 225–239. Zbl0635.04001
  2. [2] Daniels P., Kunen K., Zhou H., On the open-open game, Fund. Math. 145 (1994), no. 3, 205–220. Zbl0811.54008
  3. [3] Fremlin D., Natkaniec T., Recław I., Universally Kuratowski–Ulam spaces, Fund. Math. 165 (2000), no. 3, 239–247. Zbl0959.54010
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  6. [6] Fremlin D., Universally Kuratowski–Ulam spaces, a note from:  
  7. [7] Kucharski A., Plewik S., Game approach to universally Kuratowski–Ulam spaces, Topology Appl. 154 (2007), no. 2, 421–427.[WoS] Zbl1172.54008
  8. [8] Kucharski A., Plewik S., Inverse systems and I-favorable spaces, Topology Appl. 156 (2008), no. 1, 110–116.[WoS] Zbl1160.54007
  9. [9] Kuratowski K., Ulam S., Quelques propriétés topologiques du produit combinatoire, Fund. Math. 19 (1932), 247–251. Zbl0005.18301
  10. [10] Oxtoby J., Measure and category, Springer-Verlag, New York, 1971. 
  11. [11] Pawlikowski J., Undetermined sets of point-open games, Fund. Math. 144 (1994), 279–285. Zbl0853.54033
  12. [12] Scheepers M., Combinatorics of open covers (V): Pixley–Roy spaces of sets of reals, and ω-covers., Topology Appl. 102 (2000), no. 1, 13–31.[WoS] Zbl0960.91018
  13. [13] Szymański A., Some applications of tiny sequences, in: Proceedings of the 11th winter school on abstract analysis (Železna Rudá, 1983), Rend. Circ. Mat. Palermo (2) 1984, Suppl. no. 3, pp. 321–328. 
  14. [14] Tsaban B., Strong γ-sets and other singular spases, Topology Appl. 153 (2005), 620–639. Zbl1094.54010

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