| Title:
|
Applications of limited information strategies in Menger's game (English) |
| Author:
|
Clontz, Steven |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
58 |
| Issue:
|
2 |
| Year:
|
2017 |
| Pages:
|
225-239 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
As shown by Telgársky and Scheepers, winning strategies in the Menger game characterize $\sigma$-compactness amongst metrizable spaces. This is improved by showing that winning Markov strategies in the Menger game characterize $\sigma$-compactness amongst regular spaces, and that winning strategies may be improved to winning Markov strategies in second-countable spaces. An investigation of 2-Markov strategies introduces a new topological property between $\sigma$-compact and Menger spaces. (English) |
| Keyword:
|
Menger property |
| Keyword:
|
Menger game |
| Keyword:
|
$\sigma$-compact spaces |
| Keyword:
|
limited information strategies |
| MSC:
|
03E35 |
| MSC:
|
54D20 |
| MSC:
|
54D45 |
| MSC:
|
91A44 |
| idZBL:
|
Zbl 06773716 |
| idMR:
|
MR3666943 |
| DOI:
|
10.14712/1213-7243.2015.201 |
| . |
| Date available:
|
2017-06-13T13:23:59Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146790 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[4] Scheepers M.: Concerning $n$-tactics in the countable-finite game.J. Symbolic Logic 3 (1991), no. 3, 786–794. Zbl 0745.03039, MR 1129143 |
| Reference:
|
[5] Scheepers M.: A direct proof of a theorem of Telgársky.Proc. Amer. Math. Soc. 123 (1995), no. 11, 3483–3485. Zbl 0842.90143, MR 1273523 |
| Reference:
|
[6] Scheepers M.: Combinatorics of open covers. I. Ramsey theory.Topology Appl. 69 (1996), no. 1, 31–62. Zbl 0848.54018, MR 1378387, 10.1016/0166-8641(95)00067-4 |
| Reference:
|
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| Reference:
|
[8] Telgársky R.: On games of Topsøe.Math. Scand. 54 (1984), no. 1, 170–176. Zbl 0525.54016, MR 0753073, 10.7146/math.scand.a-12050 |
| . |
