论文标题
羽毛陀螺的补充
A supplement on feathered gyrogroups
论文作者
论文摘要
拓扑陀螺是一个旋转拓扑的陀螺仪，使得二元操作是共同连续的，并且反向映射也是连续的。结果表明，具有$ω^ω$ - 键的拓扑gyrogroup的每个紧凑子集都是可分离的，它可以推断出，如果$ g $是具有$ω^ω$ base的拓扑gyrogroup，并且是$ k $ - base，则是$ k $ - 空间，那么它是顺序的。此外，对于基于羽毛的强烈拓扑gyrogroup的特征，对于羽毛的强烈拓扑gyrogroup $ g $，我们表明，如果$ g $具有可计数的$ cs^{*} $ - 角色，那么它是可衡量的；而且还表明，$ g $有一个紧凑的分辨率，当且仅当$ g $包含紧凑型$ l $ -subgyRogroup $ h $时，吞咽紧凑型套件，使商$ g/h $是波兰空间。
A topological gyrogroup is a gyrogroup endowed with a topology such that the binary operation is jointly continuous and the inverse mapping is also continuous. It is shown that each compact subset of a topological gyrogroup with an $ω^ω$-base is metrizable, which deduces that if $G$ is a topological gyrogroup with an $ω^ω$-base and is a $k$-space, then it is sequential. Moreover, for a feathered strongly topological gyrogroup $G$, based on the characterization of feathered strongly topological gyrogroups, we show that if $G$ has countable $cs^{*}$-character, then it is metrizable; and it is also shown that $G$ has a compact resolution swallowing the compact sets if and only if $G$ contains a compact $L$-subgyrogroup $H$ such that the quotient space $G/H$ is a Polish space.
