## Antoine's Necklace

Construct a chain of components in a solid Torus . Now form a chain of solid tori in , where

via inclusion. In each component of , construct a smaller chain of solid tori embedded in that component. Denote the union of these smaller solid tori . Continue this process a countable number of times, then the intersection

which is a nonempty compact Subset of is called Antoine's necklace. Antoine's necklace is Homeomorphic with the Cantor Set.