A game and its relation to netweight and D-spaces
Gary Gruenhage; Paul Szeptycki
Commentationes Mathematicae Universitatis Carolinae (2011)
- Volume: 52, Issue: 4, page 561-568
- ISSN: 0010-2628
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topGruenhage, Gary, and Szeptycki, Paul. "A game and its relation to netweight and D-spaces." Commentationes Mathematicae Universitatis Carolinae 52.4 (2011): 561-568. <http://eudml.org/doc/246730>.
@article{Gruenhage2011,
abstract = {We introduce a two player topological game and study the relationship of the existence of winning strategies to base properties and covering properties of the underlying space. The existence of a winning strategy for one of the players is conjectured to be equivalent to the space have countable network weight. In addition, connections to the class of D-spaces and the class of hereditarily Lindelöf spaces are shown.},
author = {Gruenhage, Gary, Szeptycki, Paul},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {topological game; network; netweight; weakly separated; $D$-space; topological game; network; netweight; weakly separated subspaces; -space},
language = {eng},
number = {4},
pages = {561-568},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A game and its relation to netweight and D-spaces},
url = {http://eudml.org/doc/246730},
volume = {52},
year = {2011},
}
TY - JOUR
AU - Gruenhage, Gary
AU - Szeptycki, Paul
TI - A game and its relation to netweight and D-spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2011
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 52
IS - 4
SP - 561
EP - 568
AB - We introduce a two player topological game and study the relationship of the existence of winning strategies to base properties and covering properties of the underlying space. The existence of a winning strategy for one of the players is conjectured to be equivalent to the space have countable network weight. In addition, connections to the class of D-spaces and the class of hereditarily Lindelöf spaces are shown.
LA - eng
KW - topological game; network; netweight; weakly separated; $D$-space; topological game; network; netweight; weakly separated subspaces; -space
UR - http://eudml.org/doc/246730
ER -
References
top- Aurichi L., D-spaces, topological games and selection principles, Topology Proc. 36 (2010), 107–122. Zbl1203.54024MR2591778
- Abraham U., Shelah S., 10.1007/BF02761858, Israel J. Math. 38 (1981), 161–176. MR0599485DOI10.1007/BF02761858
- Ciesielski K., On the netweight of subspaces, Fund. Math. 117 (1983), no. 1, 37–46. Zbl0533.54003MR0712211
- van Douwen E.K., Pfeffer W.F., 10.2140/pjm.1979.81.371, Pacific J. Math. 81 (1979), no. 2, 371–377. Zbl0409.54011MR0547605DOI10.2140/pjm.1979.81.371
- Gruenhage G., 10.1090/S0002-9947-1989-0992600-5, Trans. Amer. Math. Soc. 313 (1989), 301–315. Zbl0667.54012MR0992600DOI10.1090/S0002-9947-1989-0992600-5
- Gruenhage G., 10.1090/conm/533/10502, Contemporary Mathematics 533 (2011), 13–28. Zbl1217.54025MR2777743DOI10.1090/conm/533/10502
- Gruenhage G., Moore J., Perfect compacta and basis problems in topology, in Open Problems in Topology II, Elsevier, Amsterdam, 2007, pp. 151–159.
- Soukup D., Szeptycki P.J., A counterexample in the theory of D-spaces, preprint.
- Tkachenko M.G., Chains and cardinals, Dokl. Akad. Nauk SSSR 239 (1978), no. 3, 546–549; English translation: Soviet Math. Dokl. 19 (1978), 382–385. Zbl0404.54002MR0500798
- Todorcevic S., 10.1090/conm/084, Contemporary Mathematics, 84, American Mathematical Society, Providence, Rhode Island, 1989. Zbl0659.54001MR0980949DOI10.1090/conm/084
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