论文标题
Frucht的定理在Borel环境中
Frucht's theorem in Borel setting
论文作者
论文摘要
在本文中，我们表明Frucht的定理在Borel环境中持有。更具体地说，我们证明，任何标准的鲍勒组都可以实现为Borel图的Borel Automorthism群。对我们的结构进行了轻微的修改，也可以在拓扑设置中产生以下结果：任何波兰人都可以将任何$ \ mathbf {δ^0_2} $的同构自动形态组实现。
In this paper, we show that Frucht's theorem holds in Borel setting. More specifically, we prove that any standard Borel group can be realized as the Borel automorphism group of a Borel graph. A slight modification of our construction also yields the following result in topological setting: Any Polish group can be realized as the homeomorphic automorphism group of a $\mathbf{Δ^0_2}$-graph on a Polish space.
