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Uniform Continuity

by Icebreaker
Tags: continuity, uniform
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Icebreaker
#1
Oct30-05, 02:28 PM
P: n/a
"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)."

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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Hurkyl
#2
Oct30-05, 02:54 PM
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Hah! The question forgot to state that f is supposed to be a continuous map [itex][0, +\infty) \rightarrow \mathbb{R}[/itex]!
Icebreaker
#3
Oct30-05, 02:58 PM
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Phew! It's not just me then.


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