
Re: Subspaces of limit ordinals
Posted:
Jun 30, 2014 10:34 PM


On Mon, 30 Jun 2014, David Hartley wrote: > > Elliot <marsh@panix.com> writes
> > > Let eta be a limit ordinal and A a subspace of eta. > > > > > > Is the following correct? > > > A is homeomorphic to eta iff A is an unbounded, closed subset. > > > > No. E.g. eta = omega_omega and A = {omega_n  n in omega)
> The other direction also fails. > E.g. A = eta  {omega} for any eta >= omega + omega
Since A isn't closed, A fails to fail the other direction.

