论文标题
关于当地紧凑的阿贝里安抛光群引起的等效关系
On equivalence relations induced by locally compact abelian Polish groups
论文作者
论文摘要
给定波兰组$ g $，让$ e（g）$是正确的coset等价关系$ g^ω/c（g）$，其中$ c（g）$是$ g $中所有收敛序列的组。 $ g_0 $表示，波兰$ g $的身份的连接组件表示。令$ g，h $是本地紧凑的阿贝里安抛光群。如果$ e（g）\ leq_b e（h）$，则有一个连续的同构$ s：g_0 \ rightarrow h_0 $，使得$ \ ker（s）$是非架构的。当$ g $连接并紧凑时，相反也是如此。对于$ n \ in {\ mathbb n}^+$，部分有序的集合$ p（ω）/\ mbox {fin} $可以嵌入$ e（{\ mathbb r}^n）$和$ e（{\ mathbb t}^n）$（{\ Mathbb r}^n）$（{\ Mathbb r}^n）之间的borel等价关系。
Given a Polish group $G$, let $E(G)$ be the right coset equivalence relation $G^ω/c(G)$, where $c(G)$ is the group of all convergent sequences in $G$. The connected component of the identity of a Polish group $G$ is denoted by $G_0$. Let $G,H$ be locally compact abelian Polish groups. If $E(G)\leq_B E(H)$, then there is a continuous homomorphism $S:G_0\rightarrow H_0$ such that $\ker(S)$ is non-archimedean. The converse is also true when $G$ is connected and compact. For $n\in{\mathbb N}^+$, the partially ordered set $P(ω)/\mbox{Fin}$ can be embedded into Borel equivalence relations between $E({\mathbb R}^n)$ and $E({\mathbb T}^n)$.
