Generalized Choquet spaces

摘要

We introduce an analog to the notion of Polish space for spaces of weight <= kappa, where n is an uncountable regular cardinal such that kappa( n are isomorphic by a n-Borel function. We then consider a dynamic version of the Choquet game, and show that in this case the existence of a winning strategy for player II implies the existence of a winning tactic, that is, a strategy that depends only on the most recent move. We also study a generalization of Polish ultrametric spaces where the ultrametric is allowed to take values in a set of size n. We show that in this context, there is a family of universal Urysohn-type spaces, and we give a characterization of such spaces which are hereditarily kappa-Baire.