論文

査読有り
2019年8月

Domain-complete and LCS-complete Spaces

ELECTRONIC NOTES IN THEORETICAL COMPUTER SCIENCE
  • Matthew de Brecht
  • ,
  • Jean Goubault-Larrecq
  • ,
  • Xiaodong Jia
  • ,
  • Zhenchao Lyu

345
開始ページ
3
終了ページ
35
記述言語
英語
掲載種別
研究論文(国際会議プロシーディングス)
DOI
10.1016/j.entcs.2019.07.014
出版者・発行元
ELSEVIER

We study G(delta) subspaces of continuous dcpos, which we call domain-complete spaces, and G(delta) subspaces of locally compact sober spaces, which we call LCS-complete spaces. Those include all locally compact sober spaces-in particular, all continuous dcpos-, all topologically complete spaces in the sense of Cech, and all quasi-Polish spaces-in particular, all Polish spaces. We show that LCS-complete spaces are sober, Wilker, compactly Choquet-complete, completely Baire, and circle dot-consonant-in particular, consonant; that the countably-based LCS-complete (resp., domain-complete) spaces are the quasi-Polish spaces exactly; and that the metrizable LCS-complete (resp., domain-complete) spaces are the completely metrizable spaces. We include two applications: on LCS-complete spaces, all continuous valuations extend to measures, and sublinear previsions form a space homeomorphic to the convex Hoare powerdomain of the space of continuous valuations.

Web of Science ® 被引用回数 : 3

リンク情報
DOI
https://doi.org/10.1016/j.entcs.2019.07.014
Web of Science
https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:000483310000002&DestApp=WOS_CPL
ID情報
  • DOI : 10.1016/j.entcs.2019.07.014
  • ISSN : 1571-0661
  • Web of Science ID : WOS:000483310000002

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