论文标题
de vries二元性对紧凑型Hausdorff空间之间的封闭关系的概括
A generalization of de Vries duality to closed relations between compact Hausdorff spaces
论文作者
论文摘要
石头双重性概括到类别之间的等价性$ \ mathsf {stone}^{\ Mathsf {r}} $的石头空间和封闭关系，以及$ \ Mathsf {ba}^\ Mathsf {s}布尔氏algebras和下属关系的$。在$ \ Mathsf {Stone}^{\ Mathsf {r}} $中分配等价，产生的类别等于$ \ Mathsf {Khaus}^\ Mathsf {r} $ compact hausdorff space and Claste and Claste and Claste and Clande and Clande and Clange and Clande。同样，在$ \ mathsf {ba}^\ mathsf {s} $中拆分等价产生的类别与de Vries代数的类别$ \ Mathsf {dev^s} $等同。然后，应用寓言的机制会产生$ \ mathsf {khaus}^\ mathsf {r} $等同于$ \ mathsf {dev^s} $，因此解决了最近在文献中提出的问题。 $ \ Mathsf {khaus}^\ Mathsf {r} $和$ \ Mathsf {dev^s} $之间的等价性，进一步限制了类别$ {\ Mathsf {khaus}} $ compact Hausdorff Space and dec dep $ nath subcate $ { $ \ mathsf {dev^s} $的形态满足其他条件。这可以替代双重性。这种方法的一个优点是，形态的组成是通常的关系组成。
Stone duality generalizes to an equivalence between the categories $\mathsf{Stone}^{\mathsf{R}}$ of Stone spaces and closed relations and $\mathsf{BA}^\mathsf{S}$ of boolean algebras and subordination relations. Splitting equivalences in $\mathsf{Stone}^{\mathsf{R}}$ yields a category that is equivalent to the category $\mathsf{KHaus}^\mathsf{R}$ of compact Hausdorff spaces and closed relations. Similarly, splitting equivalences in $\mathsf{BA}^\mathsf{S}$ yields a category that is equivalent to the category $\mathsf{DeV^S}$ of de Vries algebras and compatible subordination relations. Applying the machinery of allegories then yields that $\mathsf{KHaus}^\mathsf{R}$ is equivalent to $\mathsf{DeV^S}$, thus resolving a problem recently raised in the literature. The equivalence between $\mathsf{KHaus}^\mathsf{R}$ and $\mathsf{DeV^S}$ further restricts to an equivalence between the category ${\mathsf{KHaus}}$ of compact Hausdorff spaces and continuous functions and the wide subcategory $\mathsf{DeV^F}$ of $\mathsf{DeV^S}$ whose morphisms satisfy additional conditions. This yields an alternative to de Vries duality. One advantage of this approach is that composition of morphisms is usual relation composition.
