10.

(a) Let E be a subset of Rn. A point a E Rn is called a cluster point of E if En Br

(a) contains infinitely many points for every r > O. Prove that a is a cluster point of E if and only if for each r > 0, En Br

(a) \ {a} is nonempty.

(b) Prove that every bounded infinite subset of Rn has at least one cluster point