6. Let n E N.

(a) A subset E of Rn is said to be sequentially compact if and only if every sequence Xk in E has a convergent subsequence Xkj whose limit belongs to E. Prove that every compact set is sequentially compact.

(b) Prove that every sequentially compact set is closed and bounded.

(c) Prove that a set E C Rn is sequentially compact if and only if it is compact.