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Topic: G_delta
Replies: 28   Last Post: Jan 26, 2013 3:50 AM

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Butch Malahide

Posts: 894
Registered: 6/29/05
Re: G_delta
Posted: Jan 20, 2013 3:35 AM
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On Jan 20, 12:14 am, William Elliot <> wrote:
> Your proof generaly follows the proof for f in C(omega_0,S),

You mean C(omega_1,S).

> where S is regular Lindelof and ever point is G_delta, that
> f is eventually constant.  There are some differences in the
> premises of the two theorems that I'm going to puzzle upon
> and try to harmonize.

The puzzle is whether I needed to put that silly adverb "hereditarily"
in front of "Lindelof". Now that you mention it, just plain Lindelof
is good enough. I only used "hereditarily Lindelof" to show that Z is
Lindelof. It's easy to see (as shown in the last step of the argument
I posted) that Y\Z contains at most one point. It follows from the
other assumptions that Y\Z is a G_{delta}, i.e., Z is an F_{sigma} in
Y; and of course an F_{sigma} subspace of a Lindelof space is Lindelof.

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