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Let $ B \subseteq \mathbb{R}^n$ be a product of closed bounded intervals in $ \mathbb{R}$ . Fix $ N>0$ . Suppose I want to cover $ B$ with $ N$ open sets, $ U_1, \ldots, U_N$ , and get a smooth partition of unity $ \rho_1, \ldots, \rho_N$ with respect to these sets. I wasRead more