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- W2971919449 abstract "We study Gδ subspaces of continuous dcpos, which we call domain-complete spaces, and Gδ 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 Čech, 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 ⊙-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." @default.
- W2971919449 created "2019-09-12" @default.
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- W2971919449 date "2019-08-01" @default.
- W2971919449 modified "2023-10-05" @default.
- W2971919449 title "Domain-complete and LCS-complete Spaces" @default.
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- W2971919449 doi "https://doi.org/10.1016/j.entcs.2019.07.014" @default.
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