酉超阿基米德向量格
Unital hyperarchimedean vector lattices
摘要：
证明了有单位元的超阿基米德向量格范畴等价于布尔代数范畴。建立等价性所需的关键结果是，通过Yosida表示，这样的向量格自然同构于布尔（=紧Hausdorff全不连通的）空间上所有局部常数实值连续函数的向量格。我们给出了我们的主要结果的两个应用。
英文摘要：
We prove that the category of unital hyperarchimedean vector lattices is equivalent to the category of Boolean algebras. The key result needed to establish the equivalence is that, via the Yosida representation, such a vector lattice is naturally isomorphic to the vector lattice of all locally constant real-valued continuous functions on a Boolean (=compact Hausdorff totally disconnected) space. We give two applications of our main result.
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