- #1
johnqwertyful
- 397
- 14
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,∞).
It's been proven that totally bounded→bounded, so this is wrong. Why?
It's been proven that totally bounded→bounded, so this is wrong. Why?