Applications of limited information strategies in Menger's game
Commentationes Mathematicae Universitatis Carolinae (2017)
- Volume: 58, Issue: 2, page 225-239
- ISSN: 0010-2628
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topClontz, Steven. "Applications of limited information strategies in Menger's game." Commentationes Mathematicae Universitatis Carolinae 58.2 (2017): 225-239. <http://eudml.org/doc/288191>.
@article{Clontz2017,
abstract = {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.},
author = {Clontz, Steven},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Menger property; Menger game; $\sigma $-compact spaces; limited information strategies},
language = {eng},
number = {2},
pages = {225-239},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Applications of limited information strategies in Menger's game},
url = {http://eudml.org/doc/288191},
volume = {58},
year = {2017},
}
TY - JOUR
AU - Clontz, Steven
TI - Applications of limited information strategies in Menger's game
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2017
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 58
IS - 2
SP - 225
EP - 239
AB - 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.
LA - eng
KW - Menger property; Menger game; $\sigma $-compact spaces; limited information strategies
UR - http://eudml.org/doc/288191
ER -
References
top- Arhangel'skii A.V., From classic topological invariants to relative topological properties, Sci. Math. Jpn. 24 (2002), no. 1, 153–201. Zbl0994.54024MR1885790
- Hurewicz W., 10.1007/BF01216792, Math. Z. 24 (1926), no. 1, 401–421. MR1544773DOI10.1007/BF01216792
- Kunen K., Set Theory. An Introduction to Independence Proofs, Studies in Logic and the Foundations of Mathematics, 102, North-Holland Publishing Co., Amsterdam-New York, 1980. Zbl0534.03026MR0597342
- Scheepers M., Concerning -tactics in the countable-finite game, J. Symbolic Logic 3 (1991), no. 3, 786–794. Zbl0745.03039MR1129143
- Scheepers M., A direct proof of a theorem of Telgársky, Proc. Amer. Math. Soc. 123 (1995), no. 11, 3483–3485. Zbl0842.90143MR1273523
- Scheepers M., 10.1016/0166-8641(95)00067-4, Topology Appl. 69 (1996), no. 1, 31–62. Zbl0848.54018MR1378387DOI10.1016/0166-8641(95)00067-4
- Steen L.A., Seebach J.A., Counterexamples in topology, Dover Publications, Inc., Mineola, NY, 1995; reprint of the second (1978) edition. Zbl0386.54001MR1382863
- Telgársky R., 10.7146/math.scand.a-12050, Math. Scand. 54 (1984), no. 1, 170–176. Zbl0525.54016MR0753073DOI10.7146/math.scand.a-12050
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