論文

査読有り
2013年3月

Quasi-Polish spaces

ANNALS OF PURE AND APPLIED LOGIC
  • Matthew de Brecht

164
3
開始ページ
356
終了ページ
381
記述言語
英語
掲載種別
研究論文(学術雑誌)
DOI
10.1016/j.apal.2012.11.001
出版者・発行元
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

リンク情報
DOI
https://doi.org/10.1016/j.apal.2012.11.001
Web of Science
https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:000314432700010&DestApp=WOS_CPL
ID情報
  • DOI : 10.1016/j.apal.2012.11.001
  • ISSN : 0168-0072
  • eISSN : 1873-2461
  • Web of Science ID : WOS:000314432700010

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