Abstract
Around 1928, the Polish mathematician S. Mazur invented the following mathematical “game.” Player (A) is “dealt” an arbitrary subset A of a closed interval I 0 . The complementary set B = I 0 - A is dealt to player (B) The game 〈A, B〉 is played as follows: (A) chooses arbitrarily a closed interval I 1 ⊂ I 0 ; then (B) chooses a closed interval I 2 ⊂ I 1 ; then (A) chooses a closed interval I 3 ⊂ I 2; and so on, alternately. Together the players determine a nested sequence of closed intervals I n, (A) choosing those with odd index, (B) those with even index. If the set ∩ I n has at least one point in common with A, then (A) wins; otherwise, (B) wins.
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© 1980 Springer-Verlag New York Inc.
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Oxtoby, J.C. (1980). The Banach-Mazur Game. In: Measure and Category. Graduate Texts in Mathematics, vol 2. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9339-9_6
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DOI: https://doi.org/10.1007/978-1-4684-9339-9_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4684-9341-2
Online ISBN: 978-1-4684-9339-9
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