Hi

The two sets are subsets of the Euclidian space .

I need to show that

(1) is open.

(2) is open.

Definion:

I know according to the definition that a subset of is said to be open, if there for every point exist a real number given every point . Then and

Solution:

(1) and (2)

Then if both are open subsets of by definition above. Then if there exist a point x and y in both subsets, then if there still exist a epsilon > 0, then their respective Union and Intersection is also open according to the definition above.

How does that sound? Or do I need to above something more concrete?

Or do I need to add something about the union of two open sets are closed? Bu if the union of two subsets are closed, then how possible can it be open?

Best Regards.

Billy