In which metric spaces being closed and bounded implies sequentially compactness?

Question

It is well known that in an arbitrary metric space a sequentially compact subset is closed and bounded, under which hypothesis does the converse hold? Or in other words, are there spaces, other than $\mathbb{R}^n$ (or any finite dimensional Banach space) with this property?

Answer 1

Every finite dimensional normed vector space. Since each of them is isometrical isomporphic to $\mathbb{R}^N$. Conversely every infinite dimensional n.v.s. has NOT this property since the closed unit ball is closed bounded but not compact