斯通-切赫紧化与长线积的同胚
Stone-Čech compactifications and homeomorphisms of products of the long line
摘要：
本文证明$\mathcal{L}^n$的Stone-Čech紧化是空间$\bar{\mathcal{L}}^n$，其中$\bar{\mathcal{L}}$是延长的长线，即$\mathcal{L}$及其端点$\pm Ω$ .对于半闭半长线$\mathcal{L}_+$的Carnival幂的Stone-Čech紧化给出了类似的描述.作为应用，我们证明了$\cj^n$的所有同胚的群的任意扭子群（分别为. $\cl^n$）同构于对称群$S_n$（resp.半直积$(\bz/2\bz)^n\ltimes S_n$）。
英文摘要：
In this note we shall prove that the Stone-Čech compactification of $\mathcal{L}^n$ is the space $\bar{\mathcal{L}}^n$ where $\bar{\mathcal{L}}$ is the extended long line, namely, $\mathcal{L}$ together with its ends $\pm Ω$. We give a similar description for the Stone-Čech compactification of the cartesian power of the semi-closed half-long line $\mathcal{L}_+$. As an application we show that any torsion subgroup of the group of all homeomorphisms of $\cj^n$ (resp. $\cl^n$) is isomorphic to a subgroup of the symmetric group $S_n$ (resp. the semidirect product $(\bz/2\bz)^n\ltimes S_n$).
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