Definition 5.2.12: Cantor Middle Third Set
Start with the unit interval
S0 = [0, 1]Remove from that set the middle third and set
S1 = S0 \ (1/3, 2/3)Remove from that set the two middle thirds and set
S2 = S1 \ { (1/9, 2/9) (7/9, 8/9) }Continue in this fashion, where
Sn+1 = Sn \ { middle thirds of subintervals of Sn }Then the Cantor set C is defined as
C = SnFor a list of properties of the Cantor set, look at the theory of compact and perfect sets.