Date: Feb 2, 2013 11:43 AM
Author: Achimota
Subject: Re: looking for example of closed set that is *not* complete in a<br> metric space
On Saturday, February 2, 2013 4:14:23 PM UTC+8, Butch Malahide wrote:

>If (X,d) is not complete, then it has at least one closed

>subspace which is not complete, namely, (X,d) is a closed

>subspace of itself.

Understood.

On Feb 2, 1:01 am, quasi <qu...@null.set> wrote:

> Moreover, if (X,d) is not complete, it has uncountably many

> subsets which are closed but not complete.

Butch Malahide wrote

> Oh, right. At least 2^{aleph_0} of them.

Not understood. Can someone help me understand this one?

Dan

On Saturday, February 2, 2013 4:14:23 PM UTC+8, Butch Malahide wrote:

> On Feb 2, 1:01 am, quasi <qu...@null.set> wrote:

>

> > Butch Malahide wrote

>

> >

>

> > >If (X,d) is not complete, then it has at least one closed

>

> > >subspace which is not complete, namely, (X,d) is a closed

>

> > >subspace of itself.

>

> >

>

> > Moreover, if (X,d) is not complete, it has uncountably many

>

> > subsets which are closed but not complete.

>

>

>

> Oh, right. At least 2^{aleph_0} of them.