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arXiv · 2610.11417

A Universal Quasi-Polish Space

Su Gao·Qingguo Li·Hualin Miao
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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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Su Gao, Qingguo Li, Hualin Miao. 2026-10-08. A Universal Quasi-Polish Space. https://arxiv.org/abs/2610.11417

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