A Universal Quasi-Polish Space
Su Gao, Qingguo Li, Hualin Miao
Abstract
In this paper, we first construct a universal quasi-Polish space Y with the property that every quasi-Polish space is homeomorphic to a closed subspace of Y. This gives a hyperspace F(Y) of all quasi-Polish spaces which is itself a quasi-Polish space. We then prove that the collection of all Polish closed subspaces of Y forms a coanalytic, non-Borel subset of F(Y). In particular, this collection is Π11-complete.
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