This paper presents a question of topological dynamics and demonstrates that its affirmation would establish the existence of approximate equilibria in all quitting games with only normal players. A quitting game is an undiscounted stochastic game with finitely many players where every player has only two moves, to end the game with certainty or to allow the game to continue. If nobody ever acts to end the game, all players receive payoffs of 0. A player is normal if and only if by quitting alone she receives at least her min-max payoff. This proof is based on a version of the Kohlberg–Mertens [Kohlberg, E., J.-F. Mertens. 1986. On the strategic stability of equilibria. Econometrica 54(5) 1003–1037] structure theorem designed specifically for quitting games
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