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PreprintarXiv licencearXiv

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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Cite

BibTeXRIS
BibTeX
@misc{gao2026universal,
  title = {{A Universal Quasi-Polish Space}},
  author = {Su Gao and Qingguo Li and Hualin Miao},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.11417},
  eprint = {2610.11417},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.11417},
}
RIS
TY  - UNPB
TI  - A Universal Quasi-Polish Space
AU  - Su Gao
AU  - Qingguo Li
AU  - Hualin Miao
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.11417
UR  - https://arxiv.org/abs/2610.11417
AB  - 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.
ER  -