Covering Lemma: There exist $c\in \mathbb{N}$ ($c=2$ works) s.t. for any finite collection of open intervals $\{I_n\}$ there is a sub collection $\{I_{n_j}\}$, s.t. $\{I_{n_j}\}$ covers same set that $\{I_n\}$ cover and $\{I_{n_j}\}$'s can overlap at most $c$ times at any point. But it doesn't hold for squares in $\mathbb{R}\times\mathbb{R}$.
That is a homework question but I couldn't exactly understand what I should prove. What I think is since the collection is already finite they can only overlap finitely many times and that is why it seems obvious.I think I did not understand what the question exactly asks. Please some clarification!