# Mazur game

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## English[edit]

### Proper noun[edit]

- (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*A**Mazur game**, the unit interval [0,1] is initially divided into two complementary sets,*and*B*. Player 1 then chooses a closed interval in [0,1] of length and greater than zero. Player 2 then chooses an interval within the previously chosen interval, of length and greater than zero. Player 1 then chooses an interval within the previous interval, of length 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.*