Date: Feb 2, 2013 5:26 AM
Author: Butch Malahide
Subject: Re: closed but not complete
On Feb 2, 2:36 am, William Elliot <ma...@panix.com> wrote:
> On Fri, 1 Feb 2013, Butch Malahide wrote:
> > On Feb 1, 9:14 pm, William Elliot <ma...@panix.com> wrote:
> > > On Fri, 1 Feb 2013, 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?
> > > No. Assume K is a closed subset of the complete space (S,d).
> > But the original poster did not say that his metric space (X,d) was
> > complete.
> Oh, so any closed subset of Q is an example.
*Some* closed subsets of Q are examples.