Exercises
[0XC]Prerequisites:[0X0],[09T]. Let \(I\) be a set of cardinality 2, then the space \((X,d)\) is homeomorphic to the Cantor set (with the usual Euclidean metric \(|x-y|\)).
Solution 1Combining this result with [0X8] we get that the Cantor set (with its usual topology) can be endowed with an abelian group structure, where the sum and inverse are continuous functions; This makes it a topological group.