论文标题
关于Pontryagin二元性和连续逻辑的注释
A note on Pontryagin duality and continuous logic
论文作者
论文摘要
在连续的逻辑环境中，我们表现出pontryagin二元性是石材二元性的特殊情况。更具体地说，给定一个Abelian拓扑组$ a $，而$ \ nathcal f $ f $ the the Family（组）连续的同构型从$ a $到circle of circle $ \ mathbb t $，然后，查看$（a，+）$配备了配备了$ \ mathcal f $的collection $ $ m $，我们显示了locic logic $ $，我们显示了locial type $ s_ s_ s_ s_ s_ s_ s_ s_ s_ s_ s_ s_该组的Pontryagin dual $ \ Mathcal f $，后者被认为是离散组。 我们得出结论，使用Pontryagin二元性（在紧凑型和离散的Abelian群体之间），$ S_ \ Mathcal F（M）$是拓扑组$ a $的BOHR压实。
We exhibit Pontryagin duality as a special case of Stone duality in a continuous logic setting. More specifically, given an abelian topological group $A$, and $\mathcal F$ the family (group) of continuous homomorphisms from $A$ to the circle group $\mathbb T$, then, viewing $(A,+)$ equipped with the collection $\mathcal F$ as a continuous logic structure $M$, we show that the local type space $S_\mathcal F(M)$ is precisely the Pontryagin dual of the group $\mathcal F$ where the latter is considered as a discrete group. We conclude, using Pontryagin duality (between compact and discrete abelian groups), that $S_\mathcal F(M)$ is the Bohr compactification of the topological group $A$.
