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 Post subject: Existence of a (non) complete metric on an intervalPosted: Mon Jun 27, 2016 12:40 pm

Joined: Mon Jun 27, 2016 12:07 pm
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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

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