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Topic: Subspaces of limit ordinals
Replies: 8   Last Post: Jul 1, 2014 11:02 AM

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William Elliot

Posts: 2,637
Registered: 1/8/12
Re: Subspaces of limit ordinals
Posted: Jun 30, 2014 10:34 PM
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On Mon, 30 Jun 2014, David Hartley wrote:
> > Elliot <> 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.

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