自由选择的德弗里斯二元性
Choice-Free de Vries Duality
摘要：
De Vries对偶将布尔代数和Stone空间之间的Stone对偶推广到了de Vries代数（具有满足某些公理的从属关系的完备布尔代数）和紧T2空间之间的对偶。这种对偶性允许代数方法来处理与无点拓扑不同的基于区域的空间理论。在Bezhanishvili和Holliday最近提出的Stone对偶的无选择版本的基础上，建立了de Vries代数与一类de Vries空间之间的无选择对偶.我们还调查了连接与Vietoris函子的类别紧凑的T2空间和类别的紧凑的正则框架在点自由拓扑，我们提供了一个替代的，选择自由的拓扑语义的对称严格蕴涵演算Bezhanishvili等人。
英文摘要：
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.
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