论文标题
无选择的DE VRIE二元性
Choice-Free de Vries Duality
论文作者
论文摘要
de vries二重性将布尔代数和石材空间之间的石材二元性推广到De Vries代数之间的二元性（完全布尔的代数，配备了满足某些公理的下属关系）和紧凑的Hausdorff空间。这种二元性允许对基于区域的空间理论进行代数方法，与无点拓扑不同。本文以Bezhanishvili和Holliday开发的最新无选择的Stone二重性为基础，在De Vries代数与De Vries Space类别之间建立了无选择的二元性。我们还研究了与越野函数在紧凑的Hausdorff空间类别以及无点拓扑中紧凑的常规帧类别的类别上的连接，我们为Bezhanishvili等人提供了一种替代性的，无选择的拓扑性语义，以实现对称性的严格含义。
De Vries Duality generalizes Stone duality between Boolean algebras and Stone spaces to a duality between de Vries algebras (complete Boolean algebras equipped with a subordination relation satisfying some axioms) and compact Hausdorff spaces. This duality allows for an algebraic approach to region-based theories of space that differs from point-free topology. Building on the recent choice-free version of Stone duality developed by Bezhanishvili and Holliday, this paper establishes a choice-free duality between de Vries algebras and a category of de Vries spaces. We also investigate connections with the Vietoris functor on the category of compact Hausdorff spaces and with the category of compact regular frames in point-free topology, and we provide an alternative, choice-free topological semantics for the Symmetric Strict Implication Calculus of Bezhanishvili et al.
