The two sets are subsets of the Euclidian space .
I need to show that
(1) is open.
(2) is open.
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
(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?