2018/09/20 by Ruiyuan Chen, Chen, Ruiyuan · 1 citation
Mathematics · Computer Science · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #Advanced Algebra and Logic
paper · pdf · doi:10.48550/arxiv.1809.07440
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 \mathbfΠ02 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.