5.2. Compact and Perfect Sets
Example 5.2.13(a): Properties of the Cantor Set
The Cantor set is compact.The definition of the Cantor set is as follows: let
- A 0 = [0, 1]
- A n = A n-1 /
- C = A n
Hence, C is the intersection of closed, bounded sets, and therefore C is also closed and bounded. But then C is compact.