3-connected planar spaces uniquely embed in the sphere
3-connected planar spaces uniquely embed in the sphere
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3 个连通的平面空间独特地嵌入球体中
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
C. Thomassen
中科院分区：
文献类型：
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作者：
R. Bruce Richter;C. Thomassen
我们描述那些在球体中具有唯一嵌入的局部连接的球体子集 - 即，子集与其自身的每个同胚都延伸到球体的同胚。这意味着，如果 G 是球体中 3 连通图的嵌入的闭包，使得 G 中的每条单向无限路径在 G 中都有唯一的累积点，则 G 在球体中具有唯一的嵌入。特别是，三连通平面图的标准（或弗洛伊登塔尔）紧化唯一地嵌入到球体中。
We characterize those locally connected subsets of the sphere that have a unique embedding in the sphere - i.e., those for which every homeomorphism of the subset to itself extends to a homeomorphism of the sphere. This implies that if G is the closure of an embedding of a 3-connected graph in the sphere such that every 1-way infinite path in G has a unique accumulation point in G, then G has a unique embedding in the sphere. In particular, the standard (or Freudenthal) compactification of a 3-connected planar graph embeds uniquely in the sphere.