Notes on quasi-Polish spaces
Ruiyuan Chen

TL;DR
This paper provides a comprehensive overview of quasi-Polish spaces, highlighting their logical characterization and extending their theoretical framework with new proofs and Baire category techniques.
Contribution
It offers a self-contained exposition of quasi-Polish spaces, emphasizing their characterization as a0b0_2 subspaces and introducing new proofs and methods.
Findings
Quasi-Polish spaces are characterized as a0b0_2 subspaces of countable powers of Sierpinski space.
New proofs utilize Baire category techniques to deepen understanding.
The paper clarifies the logical structure and properties of quasi-Polish spaces.
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 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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Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · Advanced Algebra and Logic
