Kubicki, Grzegorz On a game of Sierpiński. (English) Zbl 0671.90110 Colloq. Math. 54, No. 2, 179-192 (1987). Let Y be a topological space, \(X\subseteq Y\). The Sierpiński game S(X,Y) proceeds as follows. Player I chooses an \(A_ 1\subseteq X\). If it is uncountable, player II answers by an uncountable \(B_ 1\subseteq A_ 1\), otherwise one sets \(B_ 1=\emptyset\). Then player I chooses an \(A_ 2\subseteq B_ 1\) and the moves continue under the same condition. Player II is declared winner if \(\cap \bar B_ n\subseteq X\). The author presents several interesting theorems concerning the determinacy and winning strategies under special conditions on X and Y. Also, a related Banach-Mazur game is discussed. Cited in 1 Document MSC: 91A99 Game theory 54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) 91A05 2-person games Keywords:topological game; infinite positional two-person game; perfect; information; uncountable Borel set; perfect subset; Sierpiński game; winning strategies; Banach-Mazur game PDFBibTeX XMLCite \textit{G. Kubicki}, Colloq. Math. 54, No. 2, 179--192 (1987; Zbl 0671.90110) Full Text: DOI