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Date: 3-8-2021
1376
Date: 31-7-2021
1353
Date: 12-5-2021
1283
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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.
REFERENCES:
Rolfsen, D. Knots and Links. Wilmington, DE: Publish or Perish Press, pp. 73-74, 1976.
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