副拓扑群的适集
Suitable sets for paratopological groups
摘要：
一个仿拓扑群$G$有一个{ \it适合集} $S$。后者意味着$S$是$G$的离散子空间，$S\cup \{e\}$是闭的，并且由$S$生成的$G$的子群$\langle S\rangle$在$G$中稠密。拓扑群中的适宜集是许多学者研究的对象。本文的目的是提供一个启动的一般调查的合适的集的paratopological群，看看在何种程度上，我们可以（通过证明命题）或不能（通过构建的例子）推广到paratopological群的结果，持有拓扑群，并提出一些具有挑战性的问题，为未来可能的研究。我们将讨论不同类的仿拓扑群何时有合适的集合。也就是说，我们考虑了满足不同分离公理的仿拓扑群（特别是可数的），仿拓扑群是类紧空间，饱和（特别是预紧）仿拓扑群。此外，我们认为持久性的财产的一组有一个合适的一套（开放或密集）的子群，产品和扩展。
英文摘要：
A paratopological group $G$ has a {\it suitable set} $S$. The latter means that $S$ is a discrete subspace of $G$, $S\cup \{e\}$ is closed, and the subgroup $\langle S\rangle$ of $G$ generated by $S$ is dense in $G$. Suitable sets in topological groups were studied by many authors. The aim of the present paper is to provide a start-up for a general investigation of suitable sets for paratopological groups, looking to what extent we can (by proving propositions) or cannot (by constructing examples) generalize to paratopological groups results which hold for topological groups, and to pose a few challenging questions for possible future research. We shall discuss when paratopological groups of different classes have suitable sets. Namely, we consider paratopological groups (in particular, countable) satisfying different separation axioms, paratopological groups which are compact-like spaces, and saturated (in particular, precompact) paratopological groups. Also we consider the permanence of a property of a group to have a suitable set with respect to (open or dense) subgroups, products and extensions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
