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A singular space related to the point-open game. (English) Zbl 0616.54021

The authors construct a completely regular space \(X_ 0\) such that player I has a winning strategy in the point-open game \(G(X_ 0)\), but \(X_ 0\) has no \(\sigma\)-closure-preserving cover by C-scattered closed sets.

MSC:

54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
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[1] Fred Galvin, Indeterminacy of point-open games, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 26 (1978), no. 5, 445 – 449 (English, with Russian summary). · Zbl 0392.90101
[2] H. J. K. Junnila, J. C. Smith, and R. Telgársky, Closure-preserving covers by small sets, Topology Appl. 23 (1986), no. 3, 237 – 262. · Zbl 0609.54019 · doi:10.1016/0166-8641(85)90042-2
[3] E. Michael, Another note on paracompact spaces, Proc. Amer. Math. Soc. 8 (1957), 822 – 828. · Zbl 0078.14805
[4] Tsugunori Nogura, A compactlike space which does not have a countable cover by \?-scattered closed subsets, Proc. Japan Acad. Ser. A Math. Sci. 59 (1983), no. 3, 83 – 84. · Zbl 0525.54014
[5] Henry Potoczny and Heikki Junnila, Closure-preserving families and metacompactness, Proc. Amer. Math. Soc. 53 (1975), no. 2, 523 – 529. · Zbl 0318.54018
[6] Rastislav Telgársky, \?-scattered and paracompact spaces, Fund. Math. 73 (1971/72), no. 1, 59 – 74. · Zbl 0226.54018
[7] Rastislav Telgársky, Spaces defined by topological games, Fund. Math. 88 (1975), no. 3, 193 – 223. · Zbl 0311.54025
[8] Rastislav Telgársky, Spaces defined by topological games. II, Fund. Math. 116 (1983), no. 3, 189 – 207. · Zbl 0558.54029
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