Solution (source code)

= Solution

Apply part (b). Since every $x_n$ belongs to the <convex set> $C$, every convex combination $\widetilde x_k$ also belongs to $C$. Since $C$ is norm closed and $\widetilde x_k\to x$ in norm, it follows that $x\in C$. Thus a <norm-closed convex set is weakly closed>.