| Title:
|
A game and its relation to netweight and D-spaces (English) |
| Author:
|
Gruenhage, Gary |
| Author:
|
Szeptycki, Paul |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
52 |
| Issue:
|
4 |
| Year:
|
2011 |
| Pages:
|
561-568 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
topological game |
| Keyword:
|
network |
| Keyword:
|
netweight |
| Keyword:
|
weakly separated |
| Keyword:
|
$D$-space |
| MSC:
|
54D20 |
| MSC:
|
54E20 |
| idZBL:
|
Zbl 1249.54052 |
| idMR:
|
MR2863999 |
| . |
| Date available:
|
2011-12-16T13:56:25Z |
| Last updated:
|
2015-02-11 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141743 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Ciesielski K.: On the netweight of subspaces.Fund. Math. 117 (1983), no. 1, 37–46. Zbl 0533.54003, MR 0712211 |
| Reference:
|
[4] van Douwen E.K., Pfeffer W.F.: Some properties of the Sorgenfrey line and related spaces.Pacific J. Math. 81 (1979), no. 2, 371–377. Zbl 0409.54011, MR 0547605, 10.2140/pjm.1979.81.371 |
| Reference:
|
[5] Gruenhage G.: Cosmicity of cometrizable spaces.Trans. Amer. Math. Soc. 313 (1989), 301–315. Zbl 0667.54012, MR 0992600, 10.1090/S0002-9947-1989-0992600-5 |
| Reference:
|
[6] Gruenhage G.: A survey of D-spaces.Contemporary Mathematics 533 (2011), 13–28. Zbl 1217.54025, MR 2777743, 10.1090/conm/533/10502 |
| Reference:
|
[7] Gruenhage G., Moore J.: Perfect compacta and basis problems in topology.in Open Problems in Topology II, Elsevier, Amsterdam, 2007, pp. 151–159. |
| Reference:
|
[8] Soukup D., Szeptycki P.J.: A counterexample in the theory of D-spaces.preprint. |
| Reference:
|
[9] 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. Zbl 0404.54002, MR 0500798 |
| Reference:
|
[10] Todorcevic S.: Partition Problems in Topology.Contemporary Mathematics, 84, American Mathematical Society, Providence, Rhode Island, 1989. Zbl 0659.54001, MR 0980949, 10.1090/conm/084 |
| . |
