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Theorem 3.39 of An Introduction to Analysis by W. R. Wade is:
Suppose that $I$ is a closed, bounded interval. If $f : I \to \mathbf{R}$ is continuous on $I$, then $f$ is uniformly continuous on $I$.
Is there such a thing as a closed, unbounded interval?
1 Answer
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Yes, for example the interval $ [0, \infty)$ is clearly unbounded, and is closed in $\mathbb{R}$ because its complement is $(-\infty, 0)$ is open.
