The set K is quite a strange set. Notice that although it contains
it does not contain any intervals.
This set is called the Cantor Middle 1/3 Set. We'll come back to it later on.
I want to show you two ways of proving this. One, directly, and the other, by deriving it from what we already know about open sets.
To see another, quicker way of proving the last Proposition, we use the following factoid:
Thus, we can use Proposition 3.15 by to prove Proposition 3.16 as folllows:
The proof is in the homework.