I am stuck with this problem. Can anyone help me out? Thank you in advance. Question was asked in NET exam 2016 June. I am a beginner of topology. I have done b) and d). Because $0$ and $1$ are limit points of $(0,1)$. If we take a sequence which converge to $0$ and $1$, this will be cauchy sequence not convergent sequence w.r.t any metric.
Which one of these are correct.
a) $(0,1)$ with the usual topology admits a metric which is complete.
b) $(0,1)$ with the usual topology admits a metric which is not complete.
c) $[0,1]$ with the usual topology admits a metric which is not complete.
d) $[0,1]$ with the usual topology admits a metric which is complete
