自由拓扑群的开子群
Open subgroups of free topological groups
摘要：
覆盖空间的理论经常被用来证明Nielsen-Schreier定理，该定理指出自由群的每个子群都是自由的。我们应用更一般的半覆盖空间理论得到了拓扑群的类似子群定理：自由Graev拓扑群的每个开子群都是自由Graev拓扑群。自由马尔可夫拓扑群的开子群是自由马尔可夫拓扑群当且仅当它是不连通的。
英文摘要：
The theory of covering spaces is often used to prove the Nielsen-Schreier theorem, which states that every subgroup of a free group is free. We apply the more general theory of semicovering spaces to obtain analogous subgroup theorems for topological groups: Every open subgroup of a free Graev topological group is a free Graev topological group. An open subgroup of a free Markov topological group is a free Markov topological group if and only if it is disconnected.
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