About: Banach game

In mathematics, the Banach game is a topological game introduced by Stefan Banach in 1935 in the second addendum to problem 43 of the Scottish book as a variation of the Banach–Mazur game. Given a subset of real numbers, two players alternatively write down arbitrary (not necessarily in ) positive real numbers such that Player one wins if and only if exists and is in . One observation about the game is that if is a countable set, then either of the players can cause the final sum to avoid the set. Thus in this situation the second player can win.