Combinatorics of open covers (III): Games, Cp(X)

Fundamenta Mathematicae

Volumn 152, Issue 3, 1997, Pages 231-254

  Scheepers, Marion ^a  

^a BOISE STATE UNIVERSITY   (United States)

Author keywords

cover; Cp(X); Countable fan tightness; Countable strong fan tightness; Infinite games; Menger property; Rothberger property; S1( , ); Sfin( , )

Indexed keywords

EID: 0038157429     PISSN: 00162736     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (23)

1. A. V. Arkhangel'skii∪, Hurewicz spaces, analytic sets and fan tightness of function spaces, Soviet Math. Dokl. 33 (1986), 396-399.
2. -, Topological Function Spaces, Kluwer, 1992.
3. J. E. Baumgartner and A. D. Taylor, Partition theorems and ultrafilters, Trans. Amer. Math. Soc. 241 (1978), 283-309.
4. A. Blass, Ultrafilter mappings and their Dedekind cuts, ibid. 188 (1974), 327-340.
5. D. Booth, Ultrafilters on a countable set, Ann. Math. Logic 2 (1970-71), 1-24.
6. P. Erdos, A. Hajnal and R. Rado, Partition relations for cardinal numbers, Acta Math. Acad. Sci. Hungar. 16 (1965), 93-196.
7. F. G al vin, Indeterminacy of point-open games, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 26 (1978), 445-448.
8. J. Gerlits and Zs. Nagy, Some properties of C(X), I, Topology Appl. 14 (1982), 151-161.
9. S. Grigorieff, Combinatorics on ideals and forcing, Ann. Math. Logic 3 (1971), 363-394.
10. W. Hurewicz, Über eine Verallgemeinerung des Boreischen Theorems, Math. Z. 24 (1925), 401-421.
11. W. Just, A. W. Miller, M. Scheepers and P. J. Szeptycki, The combinatorics of open covers II, Topology Appl. 73 (1996), 241-266.
12. J. Ketonen, On the existence of P-points, Fund. Math. 92 (1976), 91-94.
13. K. Kunen, Some points in βN, Math. Proc. Cambridge Philos. Soc. 80 (1976), 385-398.
14. C. Laflamme, Filter games and combinatorial properties of strategies, in: Contemp. Math. 192, Amer. Math. Soc., 1996, 51-67.
15. A. R. D. Mathias, Happy families, Ann. Math. Logic 12 (1977), 59-111.
16. K. Menger, Einige Überdeckungssätze der Punktmengenlehre, Sitzungsber. Wien Abt. 2a Math. Astronom. Phys. Meteorol. Mech. 133 (1924), 421-444.
17. J. Pawlikowski, Undetermined sets of point-open games, Fund. Math. 144 (1994), 279-285.
18. F. Rothberger, Eine Verschärfung der Eigenschaft C, ibid. 30 (1938), 50-55.
19. M. Sakai, Property C″ and function spaces, Proc. Amer. Math. Soc. 104 (1988), 917-919.
20. M. Scheepers, Combinatorics of open covers I: Ramsey theory. Topology Appl. 69 (1996), 31-62.
21. -, Open covers and the square bracket partition relation, Proc. Amer. Math. Soc., to appear.
22. S. Shelah, Proper Forcing, Springer, 1982.
23. R. Telgársky, On games of Topsøe, Math. Scand. 54 (1984), 170-176.