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Re: G_delta
Posted:
Jan 20, 2013 3:35 AM
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On Jan 20, 12:14 am, William Elliot <ma...@panix.com> 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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