一句话：研究哪些 dcpo 可由其 Scott 闭子集格唯一决定，并证明拟连续 dcpo 等具有 Cσ-唯一性。
本文类比 Drake 与 Thron 关于拓扑空间的结果，研究定向完备偏序集（dcpo）在全体 dcpo 中能否由其所有 Scott 闭子集构成的格完全决定，此类 dcpo 称为 Cσ-唯一。作者在 dcpo 中引入下线性元素与拟连续元素两个概念，并以此证明若干类 dcpo 具有 Cσ-唯一性，其中包括所有拟连续 dcpo，以及 Johnstone 与 Kou 给出的例子。作为推论，Cσ-唯一的 dcpo 在其 Scott 拓扑下不必是有界 sober 空间。该工作深化了 dcpo 的序结构、Scott 闭集格与 Scott 拓扑性质之间关系的理解。
In analogy to a result due to Drake and Thron about topological spaces, this paper studies the dcpos (directed complete posets) which are fully determined, among all dcpos, by their lattices of all Scott-closed subsets (such dcpos will be called $C_{\sigma}$-unique). We introduce the notions of down-linear element and quasicontinuous element in dcpos, and use them to prove that dcpos of certain classes, including all quasicontinuous dcpos as well as Johnstone's and Kou's examples, are $C_{\sigma}$-unique. As a consequence, $C_{\sigma}$-unique dcpos with their Scott topologies need not be bounded sober.Comment: 12 pages. arXiv admin note: substantial text overlap with arXiv:1607.03576
@article{paperbot405,
title = {Uniqueness of directed complete posets based on Scott closed set lattices},
author = {Dongsheng Zhao and Luoshan Xu},
journal = {Logical Methods in Computer Science},
volume = {Volume 14, Issue 2},
year = {2018},
doi = {10.23638/lmcs-14(2:10)2018}
}