Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Gao, Su, Li, Qingguo, Miao, Hualin
Institutions: Nankai University, Hunan University, Harbin Engineering University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G2480368741, G5857652478, G5870735432
OpenAlex ID: W7221158603