This website requires JavaScript.

Categorically closed countable semigroups

Taras BanakhSerhii Bardyla
摘要
In this paper we establish a connection between categorical closedness andtopologizability of semigroups. In particular, for a class $\mathsfT_{\!1}\mathsf S$ of $T_1$ topological semigroups we prove that a countablesemigroup $X$ with finite-to-one shifts is injectively $\mathsf T_{\!1}\mathsfS$-closed if and only if $X$ is $\mathsf{T_{\!1}S}$-nontopologizable in thesense that every $T_1$ semigroup topology on $X$ is discrete. Moreover, acountable cancellative semigroup $X$ is absolutely $\mathsf T_{\!1}\mathsfS$-closed if and only if every homomorphic image of $X$ is $\mathsfT_{\!1}\mathsf S$-nontopologizable. Also, we introduce and investigate a notionof a polybounded semigroup. It is proved that a countable semigroup $X$ withfinite-to-one shifts is polybounded if and only if $X$ is $\mathsfT_{\!1}\mathsf S$-closed if and only if $X$ is $\mathsf T_{\!z}\mathsfS$-closed, where $\mathsf T_{\!z}\mathsf S$ is a class of zero-dimensionalTychonoff topological semigroups. We show that polyboundedness provides anautomatic continuity of the inversion in $T_1$ paratopological groups and provethat every cancellative polybounded semigroup is a group.
展开全部
图表提取

暂无人提供速读十问回答

论文十问由沈向洋博士提出,鼓励大家带着这十个问题去阅读论文,用有用的信息构建认知模型。写出自己的十问回答,还有机会在当前页面展示哦。

Q1论文试图解决什么问题?
Q2这是否是一个新的问题?
Q3这篇文章要验证一个什么科学假设?
0
被引用
笔记
问答