Are the following are open sets in . In each case say why?
1.[0,)
2. -
3.
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.
Thanks
How are you defining open here? the natural way? open subsets of the reals are open intervals? if so,
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