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