Date: Feb 2, 2013 12:27 AM
Author: Butch Malahide
Subject: Re: closed but not complete
On Feb 1, 9:14 pm, William Elliot <ma...@panix.com> wrote:

> On Fri, 1 Feb 2013, Daniel J. Greenhoe wrote:

>

> A long title in ignarance of what he once learned in composition class.

>

> > 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.