Meager-nowhere dense games (III): Remainder strategies

摘要: Player ONE chooses a meager set and player TWO, nowhere dense per inning. They play $\omega$ many innings. ONE's consecutive choices must form (weakly) increasing sequence. TWO wins if the union of chosen sets covers sets. A strategy for which depends on knowing only uncovered part most recently is said to be remainder strategy. Theorem (among others): has winning this game played real line with its usual topology.