关于饱和或完全有界仿拓扑群的子群
On subgroups of saturated or totally bounded paratopological groups
摘要：
若每个非空集$U\subset G$的逆$U^{-1}$具有非空内部，则称一个仿拓扑群$G$是饱和的.证明了一个[第一可数]仿拓扑群$H$是一个饱和（完全有界）[阿贝尔]仿拓扑群的闭子群当且仅当$H$容许一个连续双射同态到一个（完全有界）[阿贝尔]拓扑群$G$上[使得对于单位$e$的每个邻域$U\subset H$，存在一个闭子集$F\subset G$，其中有$e\in h^{-1}(F)\subset U$ ].作为应用，我们构造了一个特征标超过其$π$ -权及其群自反特征标的仿拓扑群。给出了几个例子，证明了（对位）拓扑群是完全有界的对位拓扑群的子群，但不是正则的完全有界的对位拓扑群的子群。
英文摘要：
A paratopological group $G$ is saturated if the inverse $U^{-1}$ of each non-empty set $U\subset G$ has non-empty interior. It is shown that a [first-countable] paratopological group $H$ is a closed subgroup of a saturated (totally bounded) [abelian] paratopological group if and only if $H$ admits a continuous bijective homomorphism onto a (totally bounded) [abelian] topological group $G$ [such that for each neighborhood $U\subset H$ of the unit $e$ there is a closed subset $F\subset G$ with $e\in h^{-1}(F)\subset U$]. As an application we construct a paratopological group whose character exceeds its $π$-weight as well as the character of its group reflexion. Also we present several examples of (para)topological groups which are subgroups of totally bounded paratopological groups but fail to be subgroups of regular totally bounded paratopological groups.
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。
