```Date: Feb 1, 2013 5:25 PM
Author: J. Antonio Perez M.
Subject: Re: looking for example of closed set that is *not* complete in a<br> metric space

On Friday, February 1, 2013 6:37:40 PM UTC+2, Daniel J. Greenhoe wrote:> Let (Y,d) be a subspace of a metric space (X,d).> > > > If (Y,d) is complete, then Y is closed with respect to d. That is,> > > >   complete==>closed.> > > > Alternatively, if (Y,d) is complete, then Y contains all its limit> > points.> > > > Would anyone happen to know of a counterexample for the converse? That> > is, does someone know of any example that demonstrates that> >    closed --> complete> > is *not* true? I don't know for sure that it is not true, but I might> > guess that it is not true.> > > > Many thanks in advance,> > DanPerhaps what you want, if I understand you correctly, is within reach in a very familiar space: take the reals R with the usual, euclidean topology (or look at  R as the euclidean metric space we all know: it's the same). This is a complete space, yet the CLOSED subset [0,+oo) isn't complete...Tonio
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