(a). Show that in a general metric space the intersection of any finite collection of open sets is open. (b). Consider RE with the Euclidean metric. Prove that for any r > 0, and any x E R" the closed ball Br (x) is a closed set. (c). Consider RE with the Euclidean metric. Find an infinite collection of open sets {An JEN such that OnEN An is the closed ball B1 (0)