Construct an explicit bijection g: [0,1] --> (0,1).
Hint: One way to do it would be three parts. One for g(0), one for g(1/n) for n belongs to N and one for everything else.
A pretty standard example is this: the set of all rational numbers in (0, 1) is countable so can be "listed" . Map 0 to , 1 to , and for all rational numbers to . All irrational numbers in (0, 1) are mapped to themselves.