- ELSEVIER SCIENCE BV
We investigate some basic descriptive set theory for countably based completely quasi-metrizable topological spaces, which we refer to as quasi-Polish spaces. These spaces naturally generalize much of the classical descriptive set theory of Polish spaces to the non-Hausdorff setting. We show that a subspace of a quasi-Polish space is quasi-Polish if and only if it is Pi(0)(2) in the Borel hierarchy. Quasi-Polish spaces can be characterized within the framework of Type-2 Theory of Effectivity as precisely the countably based spaces that have an admissible representation with a Polish domain. They can also be characterized domain theoretically as precisely the spaces that are homeomorphic to the subspace of all non-compact elements of an omega-continuous domain. Every countably based locally compact sober space is quasi-Polish, hence every omega-continuous domain is quasi-Polish. A metrizable space is quasi-Polish if and only if it is Polish. We show that the Borel hierarchy on an uncountable quasi-Polish space does not collapse, and that the Hausdorff-Kuratowski theorem generalizes to all quasi-Polish spaces. (c) 2012 Elsevier B.V. All rights reserved.
Web of Science ® 被引用回数 : 39
Web of Science ® の 関連論文(Related Records®)ビュー
- DOI : 10.1016/j.apal.2012.11.001
- ISSN : 0168-0072
- eISSN : 1873-2461
- Web of Science ID : WOS:000314432700010