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Re: looking for example of closed set that is *not* complete in a
metric space
Posted:
Feb 2, 2013 11:43 AM
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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.
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