Word Count : 230

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To show that (C_0) is a Banach space, we need to prove that it is complete with respect to the norm (| \cdot |). Let (C_0) denote the space of continuous functions (f : \mathbb{R} \to \mathbb{R}) such that (\lim_{|x| \to \infty} f(x) = 0), equipped with the supremum norm [ |f|*\infty = \sup*{x \in \mathbb{R}} |f(x)|. ________ ______ __________ ________ ______ _____ ___ __________ ________ __________ ___ ______.
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