Prime Ends and Local Connectivity
Prime Ends and Local Connectivity
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DOI：
10.1112/blms/bdn061
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发表时间：
2003-09
期刊：
影响因子：
--
通讯作者：
Lasse Rempe-Gillen
中科院分区：
文献类型：
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作者：
Lasse Rempe-Gillen
设U是黎曼球面上的单连通区域，其补域K包含多个点。我们建立了一个本地连接K在一个点上的总理结束，其印象包含这一点的表征。利用Ursell和Young的一个结果，我们得到了Torhorst定理的另一种证明，即U的素端的印象至多包含两个K局部连通的点。
Let U be a simply connected domain on the Riemann sphere whose complement K contains more than one point. We establish a characterization of local connectivity of K at a point in terms of the prime ends whose impressions contain this point. Invoking a result of Ursell and Young, we obtain an alternative proof of a theorem of Torhorst, which states that the impression of a prime end of $U$ contains at most two points at which $K$ is locally connected.