Topological games: On the 50th anniversary of the Banach Mazur game
1987; Rocky Mountain Mathematics Consortium; Volume: 17; Issue: 2 Linguagem: Inglês
10.1216/rmj-1987-17-2-227
ISSN1945-3795
Autores Tópico(s)Mathematical Dynamics and Fractals
ResumoThis is an expository paper on infinite positional games of perfect information with special emphasis on their applications to set-theoretic topology.The oldest game of this kind is the Banach-Mazur game still inspiring new results, even after 50 years from its invention.Contents 1. Introduction 2. General framework for games and notation 3. The Sierpinski game 4. The Banach-Mazur game 5.The Ulam game 6.The Banach game 7. The Choquet game 8.The point-open game 9. Further topological games 10.Some other infinite games 1. Introduction.A combinatorial game in a mathematical form was described likely for the first time at the beginning of the XVII century.Bachet de Meziriac [1612] gave the following game: two players alternately choose numbers between 1 and 10; the player, on whose move the sum attains 100, is the winner.This kind of game, called Nim, was studied by Bouton , and it has an extensive literature.For a bibliography on combinatorial games the reader is referred to Fraenkel [1983, 198?] and also to Berlekamp, Conway and Guy This is an expanded version of an invited address presented at the meeting of the Wroclaw Branch of the Polish Mathematical Society on March 4, 1983, and a talk given at the Auburn Topology Conference on March 22,
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