I want to confirm the result that $f(x)$ is uniform continous on $I$ iff $| f(x)-f(y)|<|x-y|$ for each $x,y \in I$ . Is it true if $I$ is closed ? Or for every interval ?
2026-04-03 04:57:48.1775192268
Uniform continuity of $f(x)$
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This is false. Take $f(x)=2x$, for instance, on any interval.