It seems strange, but would a metric space consisting of two points, X={a,∞} be totally bounded, but not bounded? because d(a,∞)=∞. But for all ε>0, X=B(ε,a)UB(ε,∞).(adsbygoogle = window.adsbygoogle || []).push({});

It's been proven that totally bounded→bounded, so this is wrong. Why?

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# Totally bounded but not bounded

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