论文标题
合适的副学组
Suitable sets for paratopological groups
论文作者
论文摘要
副学组$ g $具有{\ it合适的集合} $ s $。后者意味着$ s $是$ g $，$ s \ cup \ {e \} $的离散子空间，而$ s $生成的子群体$ \ langle $ \ langle s \ langle s \ rangle s \ rangle $ g $是$ g $中的密集。许多作者研究了拓扑组的合适集。本文的目的是为对副学组的合适集提供一家初创企业，以寻求我们（通过证明命题）在多大程度上或不能（通过构建示例）推广到拓扑组成果，并为拓扑组构成的结果，并为可能的未来研究提出一些挑战性的问题。我们将讨论不同类别的副学组何时具有合适的集合。也就是说，我们考虑了副学组（特别是可计数），满足不同的分离公理，副学组是紧凑的空间和饱和（尤其是前术）副学组。另外，我们认为集团的财产的持久性在（开放或致密的）亚组，产品和扩展方面具有合适的集合。
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.
