论文标题
每个拓扑组都嵌入一个可分离的拓扑组中
Each topological group embeds into a duoseparable topological group
论文作者
论文摘要
如果存在可数套件$ s \ subseteq x $，则拓扑组$ x $称为$ duoseparable $，使得该单元的任何附近$ u \ u \ subseteq x $ $ s \ subseteq x $。我们构建一个分配给每个（Abelian）拓扑组$ x $ a duoseparable（Abelain-by-cyclic）拓扑组$ fx $的函数$ f $，其中包含$ x $的同构副本。实际上，函子$ f $是在Unital Topologization Magmas的类别上定义的。另外，我们还证明，每个$σ$ - compact局部紧凑的Abelian拓扑组都嵌入了杜索可行的本地紧凑型Abelian by-Countable topology群体中。
A topological group $X$ is called $duoseparable$ if there exists a countable set $S\subseteq X$ such that $SUS=X$ for any neighborhood $U\subseteq X$ of the unit. We construct a functor $F$ assigning to each (abelian) topological group $X$ a duoseparable (abelain-by-cyclic) topological group $FX$, containing an isomorphic copy of $X$. In fact, the functor $F$ is defined on the category of unital topologized magmas. Also we prove that each $σ$-compact locally compact abelian topological group embeds into a duoseparable locally compact abelian-by-countable topological group.
