Abstract
Let X be a nonempty perfect Polish space with compatible complete metric d. Fix also a basis {V n } of nonempty open sets for X. Given A ⊆ X, consider the following *-game G*(A):
U (n) i are basic open sets with diam (U (n) i <2−n,\(\overline {U_0^{(n)}} \cap \overline {U_0^{(n)}} = \emptyset\), i n Є {0,1}, and \(\overline {U_0^{(n + 1)} \cup U_1^{(n + 1)}} \subseteq U_{{i_n}}^{(n)}\) ⊆ \(U_{{i_n}}^{(n)}\). Let x ∈ X be defined by {x} = ⋂ n \(U_{{i_n}}^{(n)}\). Then I wins iff x ∈ A.
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© 1995 Springer-Verlag New York, Inc.
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Kechris, A.S. (1995). Games People Play. In: Classical Descriptive Set Theory. Graduate Texts in Mathematics, vol 156. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4190-4_21
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DOI: https://doi.org/10.1007/978-1-4612-4190-4_21
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