9. Let E be a nonempty subset of Rn.

(a) Show that a sequence x'" E E converges to some point a E E if and only if for every set U, which is relatively open in E and contains

a, there is an N E N such that Xk E U for k ~ N.

(b) Prove that a set C ~ E is relatively closed in E if and only if the limit of every sequence Xk E E which converges to a point in E satisfies limk-+ooxk E C.