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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

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Butch Malahide

Posts: 894
Registered: 6/29/05
Re: closed but not complete
Posted: Feb 2, 2013 12:27 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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.


Date Subject Author
2/1/13
Read looking for example of closed set that is *not* complete in a metric space
Achimota
2/1/13
Read Re: looking for example of closed set that is *not* complete in a
metric space
Paul
2/1/13
Read Re: looking for example of closed set that is *not* complete in a
metric space
Paul
2/1/13
Read Re: looking for example of closed set that is *not* complete in a
metric space
fom
2/1/13
Read Re: looking for example of closed set that is *not* complete in a
metric space
fom
2/2/13
Read Re: looking for example of closed set that is *not* complete in a metric space
Shmuel (Seymour J.) Metz
2/3/13
Read Re: looking for example of closed set that is *not* complete in a
metric space
fom
2/3/13
Read Re: looking for example of closed set that is *not* complete in a metric space
Shmuel (Seymour J.) Metz
2/2/13
Read Re: looking for example of closed set that is *not* complete in a
metric space
Achimota
2/2/13
Read Re: looking for example of closed set that is *not* complete in a
metric space
Butch Malahide
2/2/13
Read Re: looking for example of closed set that is *not* complete in a metric space
quasi
2/2/13
Read Re: looking for example of closed set that is *not* complete in a
metric space
Butch Malahide
2/2/13
Read Re: looking for example of closed set that is *not* complete in a
metric space
Achimota
2/2/13
Read Re: looking for example of closed set that is *not* complete in a metric space
quasi
2/3/13
Read Re: looking for example of closed set that is *not* complete in a
metric space
Achimota
2/3/13
Read Re: looking for example of closed set that is *not* complete in a
metric space
Paul
2/3/13
Read Re: looking for example of closed set that is *not* complete in a
metric space
Achimota
2/1/13
Read Re: looking for example of closed set that is *not* complete in a
metric space
Butch Malahide
2/1/13
Read Re: looking for example of closed set that is *not* complete in a
metric space
J. Antonio Perez M.
2/1/13
Read Re: looking for example of closed set that is *not* complete in a
metric space
William Hughes
2/2/13
Read Re: looking for example of closed set that is *not* complete in a
metric space
J. Antonio Perez M.
2/1/13
Read Re: looking for example of closed set that is *not* complete in a
metric space
Butch Malahide
2/1/13
Read closed but not complete
William Elliot
2/2/13
Read Re: closed but not complete
Butch Malahide
2/2/13
Read Re: closed but not complete
William Elliot
2/2/13
Read Re: closed but not complete
Butch Malahide
2/2/13
Read Re: closed but not complete
Shmuel (Seymour J.) Metz

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