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Antoine's necklace
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Antoine's necklace : ウィキペディア英語版
Antoine's necklace

In mathematics, Antoine's necklace, discovered by , is a topological embedding of the Cantor set in 3-dimensional Euclidean space, whose complement is not simply connected.
==Construction==

Antoine's necklace is constructed iteratively like so: Begin with a solid torus ''A''0 (iteration 0). Next, construct a "necklace" of smaller, linked tori that lie inside ''A''0. This necklace is ''A''1 (iteration 1). Each torus composing ''A''1 can be replaced with another smaller necklace as was done for ''A''0. Doing this yields ''A''2 (iteration 2).
This process can be repeated a countably infinite number of times to create an ''A''''n'' for all ''n''. Antoine's necklace ''A'' is defined as the intersection of all the iterations.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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