Let $I$ be a bounded interval. Is there a function $f$, which is continuous and bounded on $I$, but it's not uniformly continuous on $I$ ?
2026-03-30 00:19:55.1774829995
If $I$ is a bounded interval, is there a function on $I$ that is bounded and continuous but not uniformly continuous?
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$\sin \frac 1x$ on $(0,1]$
That function is bounded, continuous, but is not uniformly continuous.