夏威夷耳环的无芯半覆盖
A core-free semicovering of the Hawaiian Earring
摘要：
当在基环上赋予紧开拓扑的自然商拓扑时，连通和局部路连通拓扑空间$X$的连通覆盖空间可由包含$π_1(X,x)$的开正规子群的$π_1(X,x)$的子群的共轭类来分类.有已知的例子半覆盖（在意义上的Brazas），对应于不包含一个开放的正规子群的开子群。我们给出了夏威夷耳环$\mathds{H}$的一个半覆盖的例子，它对应的开子群$π_1(\mathds{H})$不包含$π_1(\mathds{H})$的{ \em any}非平凡正规子群.
英文摘要：
The connected covering spaces of a connected and locally path-connected topological space $X$ can be classified by the conjugacy classes of those subgroups of $π_1(X,x)$ which contain an open normal subgroup of $π_1(X,x)$, when endowed with the natural quotient topology of the compact-open topology on based loops. There are known examples of semicoverings (in the sense of Brazas) that correspond to open subgroups which do not contain an open normal subgroup. We present an example of a semicovering of the Hawaiian Earring $\mathds{H}$ with corresponding open subgroup of $π_1(\mathds{H})$ which does not contain {\em any} nontrivial normal subgroup of $π_1(\mathds{H})$.
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