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.
