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.