论文标题
鲁棒性，Scott的连续性和可计算性
Robustness, Scott Continuity, and Computability
论文作者
论文摘要
鲁棒性是系统分析的属性，即从（系统状态）空间的子集的完整晶格到两点晶格的单调图。鲁棒性的定义要求该空间是度量空间。强大的分析不能区分度量空间的子集及其关闭，因此可以限制限制在封闭子集的完整晶格中。当度量空间紧凑时，通过反向包含排序的封闭子集的完整晶格是W连续的，稳健的分析正是Scott连续地图。因此，还可以询问强大的分析是否可以计算（相对于可数基础）。本文的主要结果在公制空间不紧凑时建立了鲁棒性与斯科特连续性之间的关系。关键的想法是用紧凑的Hausdorff空间替换度量空间，并通过在公制空间的封闭子集的完整晶格与紧凑型Hausdorff空间的封闭子集的W-CONTINUL STICE之间的完整晶格之间进行辅助。我们通过几个涉及Banach空间的例子来证明该结果的适用性。
Robustness is a property of system analyses, namely monotonic maps from the complete lattice of subsets of a (system's state) space to the two-point lattice. The definition of robustness requires the space to be a metric space. Robust analyses cannot discriminate between a subset of the metric space and its closure, therefore one can restrict to the complete lattice of closed subsets. When the metric space is compact, the complete lattice of closed subsets ordered by reverse inclusion is w-continuous and robust analyses are exactly the Scott continuous maps. Thus, one can also ask whether a robust analysis is computable (with respect to a countable base). The main result of this paper establishes a relation between robustness and Scott continuity, when the metric space is not compact. The key idea is to replace the metric space with a compact Hausdorff space, and relate robustness and Scott continuity by an adjunction between the complete lattice of closed subsets of the metric space and the w-continuous lattice of closed subsets of the compact Hausdorff space. We demonstrate the applicability of this result with several examples involving Banach spaces.
