```Date: Feb 2, 2013 6:20 AM
Author: J. Antonio Perez M.
Subject: Re: looking for example of closed set that is *not* complete in a<br> metric space

On Saturday, February 2, 2013 12:32:40 AM UTC+2, William Hughes wrote:> On Feb 1, 11:25 pm, Tonic...@yahoo.com wrote:> > > 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,> > >> > > > Dan> > >> > > Perhaps 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> > > > Why is [0,+oo) not complete?My bad: was thinking of something complete(ly) different. Of course it is.
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