Notes on quasi-Polish spaces

Ruiyuan Chen

Notes on quasi-Polish spaces

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arxiv 1809.07440 v2 pith:SW3I3U7B submitted 2018-09-20 math.LO math.GN

Ruiyuan Chen This is my paper · ORCID

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keywords spacesquasi-polishbairebasicbrechtcategorycharacterizationcountable

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abstract

Quasi-Polish spaces were introduced by de Brecht as a possibly non-Hausdorff generalization of Polish spaces sharing many of their descriptive set-theoretic properties. We give a self-contained exposition of the basic theory of quasi-Polish spaces, based on their "logical" characterization as $\mathbf{\Pi}^0_2$ subspaces of countable powers of Sierpinski space, with several new proofs emphasizing this point of view as well as making more extensive use of Baire category techniques.

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Componentwise Polish groupoids and equivalence relations
math.LO 2025-07 conditional novelty 7.0 of 10

Every Borel-overt fiberwise quasi-Polish groupoid is Borel equivalent to an open Polish groupoid, hence to an action groupoid of a Polish group action; Borel-overt classwise Polish equivalence relations are Borel bire...

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