Antoine's necklace

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In mathematics, Antoine's necklace, discovered by Louis Antoine (1921), is an embedding of the Cantor set in 3-dimensional Euclidean space whose complement is not simply connected.

It is constructed by starting with a solid torus, replacing it by a "necklace" inside it formed of linked tori, then replacing each of these tori by another necklace inside it, and repeating this an infinite number of times.

It was used by Alexander (1924) to construct Antoine's horned sphere (similar to but not the same as Alexander's horned sphere).

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