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We investigate the pressing down game and its relation to the Banach Mazur game. In particular we show: consistently, there is a nowhere precipitous normal ideal I on
such that player nonempty wins the pressing down game of length
on I even if player empty starts.
Many properties of compacta have “textbook” definitions which are phrased in lattice-theoretic terms that, ostensibly, apply only to the full closed-set lattice of a space. We provide a simple criterion for identifying such definitions that may be paraphrased in terms that apply to all lattice...
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