Universally Kuratowski–Ulam Spaces And Open-Open Games

• Autorzy: Piotr Kalemba , Andrzej Kucharski
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

II-favorable space; uK-U space; tiny sequence

Kategorie tematyczne

• 91A44: Games involving topology or set theory
• 54G20: Counterexamples
• 54F99: None of the above, but in this section

• Wydawca: De Gruyter Open
• Czasopismo: Annales Mathematicae Silesianae
• Rocznik: 2015
• Tom: 29
• Numer: 1
• Strony: 85-92

Daty

wydano

2015-09-01

otrzymano

2015-03-10

poprawiono

2015-06-06

online

2015-09-30

Twórcy

autor

Piotr Kalemba

• Institute of Mathematics, University of Silesia, Bankowa 14 40-007 Katowice, Poland

autor

Andrzej Kucharski

• Institute of Mathematics, University of Silesia, Bankowa 14 40-007 Katowice, Poland

Bibliografia

• [1] Bartoszyński T., Combinatorial aspects of measure and category, Fund. Math. 127 (1987), no. 3, 225–239.
• [2] Daniels P., Kunen K., Zhou H., On the open-open game, Fund. Math. 145 (1994), no. 3, 205–220.
• [3] Fremlin D., Natkaniec T., Recław I., Universally Kuratowski–Ulam spaces, Fund. Math. 165 (2000), no. 3, 239–247.
• [4] Fremlin D., Miller A.W., On some properties of Hurewicz, Menger and Rothberger, Fund. Math. 129 (1988), 17–33.
• [5] Just W., Miller A.W., Scheepers M., Szeptycki P.J., The combinatorics of open covers (II), Topology Appl. 73 (1996), 241–266.[WoS]
• [6] Fremlin D., Universally Kuratowski–Ulam spaces, a note from:
• [7] Kucharski A., Plewik S., Game approach to universally Kuratowski–Ulam spaces, Topology Appl. 154 (2007), no. 2, 421–427.[WoS]
• [8] Kucharski A., Plewik S., Inverse systems and I-favorable spaces, Topology Appl. 156 (2008), no. 1, 110–116.[WoS]
• [9] Kuratowski K., Ulam S., Quelques propriétés topologiques du produit combinatoire, Fund. Math. 19 (1932), 247–251.
• [10] Oxtoby J., Measure and category, Springer-Verlag, New York, 1971.
• [11] Pawlikowski J., Undetermined sets of point-open games, Fund. Math. 144 (1994), 279–285.
• [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]
• [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] Tsaban B., Strong γ-sets and other singular spases, Topology Appl. 153 (2005), 620–639.

Identyfikatory

DOI

10.1515/amsil-2015-0007