Construct a chain of components in a solid torus . Now thicken each component of slightly to 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.