Antoine's necklace

First iteration

Second iteration

Renderings of Antoine's necklace

In mathematics, Antoine's necklace is a topological embedding of the Cantor set in 3-dimensional Euclidean space, whose complement is not simply connected. It also serves as a counterexample to the claim that all Cantor spaces are ambiently homeomorphic to each other. It was discovered by Louis Antoine (1921).^[1]