I know that every subspace of $R^k$ is Lindelöf, i.e.: If G is a subspace of $R^k$, then any open covering of G has a countable sub-covering.
I was thinking whether it is true that, given G a subspace of $R^k$ any closed covering of G (covered by closed boxes, (coordinate of each dimension has the form [a,b], $(-\infty, a]$, or $[a,+\infty$)) has a countable sub-covering? in the case k=1, it seems true to me.