"Suppose f:[0, inf) -> R is such that f is uniformly continuous on [a, inf) for some a>0. Prove that f is uniformly continuous on [0, inf)."(adsbygoogle = window.adsbygoogle || []).push({});

But this is not true, is it? Consider the function

[tex]f(x)=\left\{\begin{array}{cc}x &\mbox{ if }x\geq 1\\ \frac{1}{x-1} &\mbox{ if }x<1\end{array}\right[/tex]

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# Uniform Continuity

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