论文标题
$ g $ - 兼容的拓扑团体
$G$-compactness for topological groups with operations
论文作者
论文摘要
众所周知，对于Hausdorff拓扑组$ x $，$ x $中的收敛序列的限制定义了$ \ lim $表示的函数，从$ x $ to $ x $的所有收敛序列中表示。 Connor和Grosse-Erdmann已通过使用所有真实序列的向量空间的线性子空间中定义的任意线性函数$ G $替换$ \ lim $来修改此概念。最近，一些作者将该概念扩展到了拓扑组设置，并介绍了$ g $ - 续签，$ g $ compactness和$ g $连接的概念。在本文中，我们证明了有关拓扑组的不同类型的$ G $ compactness，其中包括拓扑组，没有身份的拓扑环，R模型，Lie代数，Jordan代数等。
It is well known that for a Hausdorff topological group $X$, the limits of convergent sequences in $X$ define a function denoted by $\lim$ from the set of all convergent sequences in $X$ to $X$. This notion has been modified by Connor and Grosse-Erdmann for real functions by replacing $\lim$ with an arbitrary linear functional $G$ defined on a linear subspace of the vector space of all real sequences. Recently some authors have extended the concept to the topological group setting and introduced the concepts of $G$-continuity, $G$-compactness and $G$-connectedness. In this paper we prove some results on different types of $G$-compactness for topological group with operations which include topological groups, topological rings without identity, R-modules, Lie algebras, Jordan algebras, and many others.
