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Generalized Choquet spaces

Samuel CoskeyPhilipp Schlicht — 2016

Fundamenta Mathematicae

We introduce an analog to the notion of Polish space for spaces of weight ≤ κ, where κ is an uncountable regular cardinal such that κ < κ = κ . Specifically, we consider spaces in which player II has a winning strategy in a variant of the strong Choquet game which runs for κ many rounds. After discussing the basic theory of these games and spaces, we prove that there is a surjectively universal such space and that there are exactly 2 κ many such spaces up to homeomorphism. We also establish a Kuratowski-like...

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