论文标题
拓扑组完全断开的半群压缩
Totally disconnected semigroup compactifications of topological groups
论文作者
论文摘要
我们介绍了一个内向的布尔代数$ \ cal b $的概念的封闭式和开放的子集$ g $，表明相关的石头空间$（ν_{c al {\ cal b} g，v，ν_{\ cal b}）$是$ g $的完全脱颖而出的份额，并将其完全脱颖而出。我们识别并研究了通用完全断开的半群紧凑型，通用的完全断开的半足型半群紧凑型和$ g $的通用完全断开的群体紧凑型。我们的主要结果独立于Gelfand理论和（通常是非全面断开的）通用压实的众所周知的属性$ g^{luc} $，$ g^{wap} $和$ g^{ap} $，尽管我们确实采用了gelfand理论来澄清这些熟悉的通用压实彼此之间的关系之间的关系。
We introduce the notion of an introverted Boolean algebra $\cal B$ of closed-and-open subsets of a topological group $G$, show that the associated Stone space $(ν_{\cal B} G, ν_{\cal B})$ is a totally disconnected semigroup compactification of $G$, and show that every totally disconnected semigroup compactification of $G$ takes this form. We identify and study the universal totally disconnected semigroup compactification, the universal totally disconnected semitopological semigroup compactification and the universal totally disconnected group compactification of $G$. Our main results are obtained independently of Gelfand theory and well-known properties of the (typically non-totally disconnected) universal compactifications $G^{LUC}$, $G^{WAP}$ and $G^{AP}$, though we do employ Gelfand theory to clarify the relationship between these familiar universal compactifications and their totally disconnected counterparts.
