0
$\begingroup$

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

  • 3
    This doesn't make sense. If $\sup f(X)=\infty$, then $f$ is not bounded.2012-12-09
  • 0
    See here http://math.stackexchange.com/questions/254224/continuity-and-boundedness/254316#2543162012-12-09
  • 0
    @AlexYoucis I think (s)he probably means $X$ a bounded subset of $\mathbb{R}$, not $f$ bounded2012-12-09

3 Answers 3