I've tried to think this, help would be appreciated to get me going a gain.

If we have two nonempty open set so that(two separate sets). How could I show that complement of union A and B is also nonempty, .

I'm thinking something like, because the complement is so because its R^n there must be some points that belong to that complement. But basicly I think that don't work (just to say because it's R^n) because I have show that it (complement of the union is nonempty) follows from the notion that A,B are open nonempty sets.

Any ideas and help? Thanks!