连通性的序贯定义
Sequential Definitions of Connectedness
摘要：
一个拓扑群$X$称为连通的，如果它的开闭子集只有全空间$X$和零集$\emptyset$。拓扑群的子集是连通的，如果子空间是连通的。我们说$X$的子集$A$是$G$ -序贯连通的，如果$A$的唯一子集是$G$ -序贯开和$G$ -序贯闭的，相对于$A$的相对$G$ -序贯开和$G$ -序贯闭子集，是$A$的开子集和闭子集是$A$和零集$\emptyset$。我们研究了序列收敛的定义的改变对$X$的子集的序列连通性结构的影响，通过序列闭包的集合的意义下的$G$ -序列闭包。当G = lim时，拓扑群的序列连通性是这一推广的特殊情况。
英文摘要：
A topological group $X$ is called connected if the only subsets which are both open and closed are the whole space $X$ and the null set $\emptyset$. A subset of a topological group is connected if the subspace is connected. We say that a subset $A$ of $X$ is $G$-sequentially connected if the only subsets of $A$ which are both $G$-sequentially open and $G$-sequentially closed, with respect to the relative $G$-sequentially open and $G$-sequentially closed subsets of $A$, are open and closed subsets of $A$ are $A$ and the null set, $\emptyset$. We investigate the impact of changing the definition of convergence of sequences on the structure of sequential connectedness of subsets of $X$ via sequential closure of sets in the sense of $G$-sequential closure. Sequential connectedness for topological groups is a special case of this generalization when G = lim.
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