We unify several extensions of the classic Stone duality due to Grätzer, Hofmann–Lawson and Jung–Sünderhauf. Specifically, we show that \(\cup \)-bases of locally compact sober spaces are dual to \(\prec \)-distributive \(\vee \)-predomains, where \(\prec \) is a relation representing compact containment.

中文翻译：

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Grätzer–Hofmann–Lawson–Jung–Sünderhauf对偶

由于Grätzer，Hofmann-Lawson和Jung-Sünderhauf，我们统一了经典Stone对偶的几个扩展。具体来说，我们证明了局部紧凑型清醒空间的\（\ cup \）-基对\（\ prec \）- distributive \（\ vee \）- predomains是双重的，其中\（\ prec \）是表示紧凑型的关系遏制。