Are the following are open sets in . In each case say why?
For 1. I know its not an open set because the complement is open so [0,) is closed.
But need help for 2 and 3.
yes, 1. is closed, because its compliment is open.
For 2, notice that you have the set:
For 3, is a set of points on the real line... but be careful, is dense in , so you're going to want to come from the perspective of boundary points, etc