Abstract

The maximal point space of a domain (resp. algebraic domain) with the Scott topology is Choquet complete. Thus, not every T₁ topological space can be represented as the maximal point space of some algebraic domain equipped with the Scott topology. However, in this paper, we prove that: (1) Every T₁ topological space is homeomorphic to the set of all maximal points of some algebraic domain equipped with the relative lower topology. (2) Bounded complete domains endowed with the lower topology are Choquet complete.

中文翻译：

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拓扑空间的下拓扑代数域模型

摘要

具有 Scott 拓扑的域（或代数域）的最大点空间是 Choquet 完备的。因此，并非每个T ₁拓扑空间都可以表示为某些配备 Scott 拓扑的代数域的最大点空间。然而，在本文中，我们证明： (1) 每个T ₁拓扑空间同胚于具有相对较低拓扑的某个代数域的所有极大点的集合。(2) 具有较低拓扑结构的有界完备域是 Choquet 完备域。