论文标题
de vries权力和接近示例代数
De Vries powers and proximity Specker algebras
论文作者
论文摘要
由de vries duality [9]，紧凑型Hausdorff空格的类别$ {\ sf khaus} $双重等同于de vries代数的类别$ {\ sf dev} $。在[5]中，开发了$ {\ sf khaus} $的替代二元性，在该二元中，de vries代数被接近的baer-specker代数代替。与每个紧凑的Hausdorff空间相关联的函子，通过将一个完全有序的域的布尔幂的概念推广到de vries幂的近端来描述一个邻近的baer-specker代数。因此，$ {\ sf dev} $等效于近距离baer-specker代数的类别$ {\ sf pbsp} $。等价是通过通过$ {\ sf khaus} $获得的，因此不可选择。在本文中，我们给出了这种等价性的直接代数证明，这是无选择的。为此，我们给出了完全有序域的De Vries权力的另一种无选择的描述。
By de Vries duality [9], the category ${\sf KHaus}$ of compact Hausdorff spaces is dually equivalent to the category ${\sf DeV}$ of de Vries algebras. In [5] an alternate duality for ${\sf KHaus}$ was developed, where de Vries algebras were replaced by proximity Baer-Specker algebras. The functor associating with each compact Hausdorff space a proximity Baer-Specker algebra was described by generalizing the notion of a boolean power of a totally ordered domain to that of a de Vries power. It follows that ${\sf DeV}$ is equivalent to the category ${\sf PBSp}$ of proximity Baer-Specker algebras. The equivalence is obtained by passing through ${\sf KHaus}$, and hence is not choice-free. In this paper we give a direct algebraic proof of this equivalence, which is choice-free. To do so, we give an alternate choice-free description of de Vries powers of a totally ordered domain.
