Since I've had a marked disability to write proofs I wanted to run this by you guys to insure that it was correct before I moved on.
First I prove that is not open
Since there should exist some interval so because we are using the euclidean topology. Then there should also be or . However, .
Then we need to prove that it is not closed. To do such We prove that the compliment is not open.
. To prove that this is not open we just need to prove that one of the members of the union is not open. Using the same strategy then on let or . Then find the element and see that it is not in . Thus proving that the compliment is not open and that the set is not open nor closed.
Is this correct?