Some of the covering properties of spaces as defined in Parts I and II are here characterized by games. These results, applied to function spaces of countable tightness, give new characterizations of countable fan tightness and countable strong fan tightness. In particular, each of these properties is characterized by a Ramseyan theorem.
@article{bwmeta1.element.bwnjournal-article-fmv152i3p231bwm,
author = {Marion Scheepers},
title = {Combinatorics of open covers (III): games, Cp (X)},
journal = {Fundamenta Mathematicae},
volume = {154},
year = {1997},
pages = {231-254},
zbl = {0884.90149},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv152i3p231bwm}
}
Scheepers, Marion. Combinatorics of open covers (III): games, Cp (X). Fundamenta Mathematicae, Tome 154 (1997) pp. 231-254. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv152i3p231bwm/
[00000] [1] A. V. Arkhangel'skiĭ, Hurewicz spaces, analytic sets and fan tightness of function spaces, Soviet Math. Dokl. 33 (1986), 396-399. | Zbl 0606.54013
[00001] [2] A. V. Arkhangel'skiĭ, Topological Function Spaces, Kluwer, 1992.
[00002] [3] J. E. Baumgartner and A. D. Taylor, Partition theorems and ultrafilters, Trans. Amer. Math. Soc. 241 (1978), 283-309. | Zbl 0386.03024
[00003] [4] A. Blass, Ultrafilter mappings and their Dedekind cuts, Trans. Amer. Math. Soc. 188 (1974), 327-340. | Zbl 0305.02065
[00004] [5] D. Booth, Ultrafilters on a countable set, Ann. Math. Logic 2 (1970-71), 1-24. | Zbl 0231.02067
[00005] [6] P. Erdős, A. Hajnal and R. Rado, Partition relations for cardinal numbers, Acta Math. Acad. Sci. Hungar. 16 (1965), 93-196. | Zbl 0158.26603
[00006] [7]G F. Galvin, Indeterminacy of point-open games, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 26 (1978), 445-448. | Zbl 0392.90101
[00007] [8] J. Gerlits and Zs. Nagy, Some properties of C(X) I, Topology Appl. 14 (1982), 151-161.
[00008] [9] S. Grigorieff, Combinatorics on ideals and forcing, Ann. Math. Logic 3 (1971), 363-394. | Zbl 0328.02041
[00009] [10]H W. Hurewicz, Über eine Verallgemeinerung des Borelschen Theorems, Math. Z. 24 (1925), 401-421. | Zbl 51.0454.02
[00010] [11] W. Just, A. W. Miller, M. Scheepers and P. J. Szeptycki, The combinatorics of open covers II, Topology Appl. 73 (1996), 241-266. | Zbl 0870.03021
[00011] [12] J. Ketonen, On the existence of P-points, Fund. Math. 92 (1976), 91-94. | Zbl 0339.54035
[00012] [13] K. Kunen, Some points in βN, Math. Proc. Cambridge Philos. Soc. 80 (1976), 385-398. | Zbl 0345.02047
[00013] [14] C. Laflamme, Filter games and combinatorial properties of strategies, in: Contemp. Math. 192, Amer. Math. Soc., 1996, 51-67. | Zbl 0854.04004
[00014] [15] A. R. D. Mathias, Happy families, Ann. Math. Logic 12 (1977), 59-111.
[00015] [16] K. Menger, Einige Überdeckungssätze der Punktmengenlehre, Sitzungsber. Wien Abt. 2a Math. Astronom. Phys. Meteorol. Mech. 133 (1924), 421-444. | Zbl 50.0129.01
[00016] [17]P J. Pawlikowski, Undetermined sets of point-open games, Fund. Math. 144 (1994), 279-285. | Zbl 0853.54033
[00017] [18] F. Rothberger, Eine Verschärfung der Eigenschaft C, Fund. Math. 30 (1938), 50-55. | Zbl 64.0622.01
[00018] [19] M. Sakai, Property C'' and function spaces, Proc. Amer. Math. Soc. 104 (1988), 917-919. | Zbl 0691.54007
[00019] [20] M. Scheepers, Combinatorics of open covers I: Ramsey theory, Topology Appl. 69 (1996), 31-62. | Zbl 0848.54018
[00020] [21] M. Scheepers, Open covers and the square bracket partition relation, Proc. Amer. Math. Soc., to appear. | Zbl 0884.03048
[00021] [22] S. Shelah, Proper Forcing, Springer, 1982.
[00022] [23] R. Telgársky, On games of Topsœ, Math. Scand. 54 (1984), 170-176. | Zbl 0525.54016