Let n ∈ N.
a) A subset E of Rn is said to be sequentially compact if and only if every sequence in E has a convergent subsequence. 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 ⊂ Rn is sequentially compact if and only if it is compact.