Notes on 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 ${\mathbf{\Pi }}_2^0$ 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.

20 pages; simplified proof of game characterization; various minor fixes

References in corpus (1)

• On the commutativity of the powerspace constructions

Cited by in corpus (3)

• Decompositions and measures on countable Borel equivalence relations
• Borel and analytic sets in locales
• Representing Polish groupoids via metric structures