Consider the following statement:
Every compact subset of an open convex set $B\subset\mathbb{R}^k$ can be covered by finitely many cubes having edges parallel to the coordinate directions $e_1,...,e_k$.
How is the statement translated for the case $k=1$? And what's the relation with the fact that "There are many compact subsets of $\mathbb{R}$ that are not the union of finitely many closed intervals'' as explained here?