
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.

