Construct a chain of components in a solid Torus . Now form a chain of solid tori in ,
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
which is a nonempty compact Subset of is called Antoine's necklace. Antoine's necklace is Homeomorphic
with the Cantor Set.
See also Alexander's Horned Sphere, Necklace
Rolfsen, D. Knots and Links. Wilmington, DE: Publish or Perish Press, pp. 73-74, 1976.
© 1996-9 Eric W. Weisstein