English Dictionary

Mazur game

固有名詞

(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.

日本語の意味

(位相数学) ポーランドの数学者マズールによって考案された、第一類集合と第二類集合の違いを示すための位相ゲーム。

During the seminar, the professor used the Mazur game to demonstrate the distinction between first-category and second-category sets.

セミナーの間、教授はマズールが考案した位相ゲームを用いて第一類集合と第二類集合の区別を示した。

意味（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 <1/2 and greater than zero. Player 2 then chooses an interval within the previously chosen interval, of length <1/3 and greater than zero. Player 1 then chooses an interval within the previous interval, of length <1/4 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.