Is there exist an $f:X\to \mathbb{R}$ where $\sup f(X)= +\infty$ and $f$ is uniformly continuous on $X$ where X is bounded? I think there should not be existing such $f$ as the change of the value of $f$ too quick
Is there exist such $f$
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3This doesn't make sense. If $\sup f(X)=\infty$, then $f$ is not bounded. – 2012-12-09
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0See here http://math.stackexchange.com/questions/254224/continuity-and-boundedness/254316#254316 – 2012-12-09
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0@AlexYoucis I think (s)he probably means $X$ a bounded subset of $\mathbb{R}$, not $f$ bounded – 2012-12-09