Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Butch Malahide

Posts: 894
Registered: 6/29/05
Re: looking for example of closed set that is *not* complete in a
metric space

Posted: Feb 2, 2013 12:32 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Feb 1, 11:10 pm, "Daniel J. Greenhoe" <dgreen...@yahoo.com> wrote:
> On Saturday, February 2, 2013 12:52:55 AM UTC+8, peps...@gmail.com wrote:
> > ...To say that a space is "closed"
> > (as in your statement "closed -> complete") doesn't really mean anything.
> > To make progress replace "closed -> complete" by something more
> > formal and rigorous and precise.

>
> This is certainly good advice and many apologies for my sloppy original posting. Is the following any better?...
>
> Let (X,d) be a metric space.
> Let T be the topology induced by d and
> (X,T) be the resulting topological space.
> Let Y be a subset of X.
> Then
>   (Y,d) is complete ==> Y is closed in (X,d).
> Alternatively,
>   (Y,d) is complete ==> Y is closed in (X,T).
>
> But what about the converse? That is, is this true?
>   Y is closed in (X,d) ?==>? (Y,d) is complete


Is (X,d) complete? If (X,d) is a complete metric space, then every
closed subspace of (X,d) is complete. 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.


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

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.