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Given a closed rectangle $R$ are there closed squares $(S_{i})_{1\leq i\leq n}$ such that $R=\underset{1\leq i\leq n}{\cup}S_{i}$ and $S_{i}^{\circ}\cap S_{j}^{\circ}=\varnothing$ for $i\neq j$ ?

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    Thanks to you all, I'll try to find those proofs. Apparently, it wasn't as trivial as I thought it was.2012-04-27

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