Mazur game

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Noun[edit]

Mazur game (plural Mazur games)

  1. (topology) A topological game invented by the Polish mathematician Mazur in order to illustrate the difference between sets of the first category and second category.
    • In the Mazur game, the unit interval [0,1] is initially divided into two complementary sets, A and B. Player 1 then chooses a closed interval in [0,1] of length \le {1 \over 2} and greater than zero. Player 2 then chooses an interval within the previously chosen interval, of length \le {1 \over 3} and greater than zero. Player 1 then chooses an interval within the previous interval, of length \le {1\over 4} and greater than zero, and so on. After infinitely many steps, the intersection of all the chosen intervals is a single point: if it falls within set A, then player 1 wins; if it falls within set B, player 2 wins.