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Topic: looking for example of closed set that is *not* complete in a metric space
Replies: 26   Last Post: Feb 3, 2013 11:06 AM

 Messages: [ Previous | Next ]
 Achimota Posts: 255 Registered: 4/30/07
Re: looking for example of closed set that is *not* complete in a
metric space

Posted: Feb 2, 2013 11:43 AM

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.

Date Subject Author
2/1/13 Achimota
2/1/13 Paul
2/1/13 Paul
2/1/13 fom
2/1/13 fom
2/2/13 Shmuel (Seymour J.) Metz
2/3/13 fom
2/3/13 Shmuel (Seymour J.) Metz
2/2/13 Achimota
2/2/13 Butch Malahide
2/2/13 quasi
2/2/13 Butch Malahide
2/2/13 Achimota
2/2/13 quasi
2/3/13 Achimota
2/3/13 Paul
2/3/13 Achimota
2/1/13 Butch Malahide
2/1/13 J. Antonio Perez M.
2/1/13 William Hughes
2/2/13 J. Antonio Perez M.
2/1/13 Butch Malahide
2/1/13 William Elliot
2/2/13 Butch Malahide
2/2/13 William Elliot
2/2/13 Butch Malahide
2/2/13 Shmuel (Seymour J.) Metz