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If $ f \in C_0^\infty=\{ g: g\in C^\infty, \lim_{|x|\rightarrow \infty}g(x)=0\}$, then is $f$ uniformly continuous on $\mathbb R$? ($ f : \mathbb R \to \mathbb R $)

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    I do not think that this is a duplicate of that question.2012-06-10

1 Answers 1

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HINTs

  1. A continuous function on a compact interval is uniformly continuous.
  2. $\lim_{|x| \to \infty} f(x) = 0$ means that $\forall \epsilon...$
  3. Split up the domain to use these two properties.