4 a. (10) Let $E \subset \mathbb{R}$ and suppose that $f_n \to f$ uniformly on E, as $n \to \infty$. If each $f_n$ is continuous, then f is continuous.
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4 a. (10) Let $E \subset \mathbb{R}$ and suppose that $f_n \to f$ uniformly on E, as $n \to \infty$. If each $f_n$ is continuous, then f is continuous.